Thanks to the explosive growth of massive data brought by the development of astronomicalobservation technology，cosmology has achieved rapid and breakthrough development in the pasttwo decades. This article combines the physical theories of cosmology and new astronomicalobservation data，two works have been carried out. The first one tests the cosmic distance dualrelationship (CDDR)，and the second one proposes a new method to test the cosmological modelbased on the Alcock-Paczyński effect.CDDR closely links two basic cosmological distances (luminosity distance d L and angulardiameter distance d A ): η(z) ≡ (1 + z) 2 d A (z)/d L (z) = 1. So far，a large number of cosmologicalresearch results are based on the assumption that CDDR is valid，and the obvious deviation fromCDDR will mean the old theory is incomplete，and at the same time it shows the possibility of theemergence of new physics. Therefore，it is a basic and important work to test whether CDDR isvalid. In the past，relevant research on CDDR test is based on the assumption of Ω K that equals tozero，this article does not assume that the space curvature is zero，and based on the new quasardata set and strong gravitational lens data set，a more accurate test of CDDR is carried out. In thisarticle，CDDR is parameterized into three forms 1+η 0 z，1+η 1 z+η 2 z 2 ，1+η 3 z/(1+z)，and bothsingular isothermal sphere (SIS) model and general model (non-SIS) of the strong gravitationallens are considered. The results show that the observed data basically support CDDR but slightlytend to be η(z) < 1. This result does not strongly violate the validity of CDDR. For the slightdeviation of CDDR, in addition to considering the possible errors in the existing theoretical system,other factors should also be considered. In this paper, by checking other curvature values, it isfound that the value of space curvature has a certain influence on the CDDR test. In addition, dueto the reason that the strong gravitational lens data set is not complete，the number is small andcomes from different observations，so its systematic error will have a certain impact on the testresults. Therefore, choosing an appropriate space curvature value and adopting a more complete data set can improve the accuracy and reliability of the test results.The traditional method that use Alcock-Paczyński effect to measure the geometry of the u-niverse and test the cosmological model needs to rely on the observation source with a specificspherical distribution. Due to the lack of sufficient understanding of the evolution process of theobservation source and the influence of redshift distortion on the test results，the traditional testhas certain limitations. This paper uses a new test method based on the Alcock-Paczyński effec-t. The new method does not depend on the evolution of the observation source and will not beaffected by redshift distortion. Based on this new method，we use the quasar data of the SloanDigital Sky Survey SDSS-IV to test three cosmological models under the Friedmann-Lema??tre-Robertson-Walker (FLRW) metric: standard ΛCDM model，Einstein-de Sitter model and Rh=ctmodel. The final result shows that Einstein-de Sitter model is largely excluded, ΛCDM model isbasically consistent with the data，and the Rh=ct model is the best fit with the data. With thecontinuous completion of future quasar data sets, the accuracy, reliability and application scope ofthis method will continue to improve and expand.