In urban canyon environments, the multi-path effect and non-line-of-sight phenomenon significantly affect the positioning accuracy of GNSS, which in turn impacts the positioning performance of the INS/GNSS integrated navigation system. Traditional INS/GNSS integrated systems, however, struggle to accurately determine the rapidly changing GNSS measurement noise in such environments. To improve the robustness and estimation accuracy of the integrated navigation system, this paper proposes a robust factor graph optimization algorithm based on adaptive MCMC. The main issue addressed is the inaccuracy of measurement noise covariance in traditional factor graph optimization, which reduces state estimation accuracy. First, adaptive MCMC is introduced into the factor graph optimization framework, incorporating both prior and posterior stages. In the prior stage, the MCMC algorithm transforms posterior probability sampling into the product of prior and likelihood probability sampling, with an adaptive strategy enhancing sampling efficiency to obtain the posterior sample set. In the posterior stage, KL divergence minimizes the difference between the approximate and true posterior, allowing for accurate estimation of GNSS time-varying measurement noise covariance. Additionally, an innovation chi-square detection algorithm is used to detect and eliminate outliers by constructing hypothesis test statistics and identifying abnormal boundary values. The proposed method effectively estimates GNSS time-varying measurement noise while reducing outlier interference. Simulation and field tests of the INS/GNSS integrated navigation system show that the proposed method reduces horizontal positioning root mean square error by 20.4%, 11.9%, and 71.6%, 25.2% respectively compared to the standard factor graph optimization and the robust adaptive factor graph optimization algorithms based on variational Bayesian, respectively. The method also demonstrates improved robustness.