Abstract: Based on the mean-variance criterion, this paper studies the optimal investment strategy selection with the influences of liability and ambiguity aversion. The liability is defined by a stochastic differential equation, and the financial market consists of one risk-free asset and one risky asset. The prices of liability and risky asset are dependent, and the dependence is reflected by the correlation between two Brownian motions. By using the theory of stochastic control and stochastic dynamic programming, we establish the Hamilton-Jacobi-Bellman-Issacs (HJBI) equation of the value function under the mean-variance criteria. Furthermore, by using stochastic optimization theory, the explicit solution for the robust optimal investment strategy is obtained. Finally, the effect of model parameters on the global robust optimal investment strategy is discussed through numerical experiments, and the research results can effectively guide the investment decision in reality.