In reality, when facing a multi-period asset-liability portfolio selection problem, the risk aversion attitude of a mean-variance investor may depend on the wealth level and liability level. Thus, in this paper, we propose a state-dependent risk aversion model for the investor, in which risk aversion is a linear function of current wealth level and current liability level. Due to the time inconsistency of the resulting multi-period asset-liability mean-variance model, we investigate its time-consistent portfolio policy by solving a nested mean-variance game formulation. We derive the analytical time-consistent portfolio policy, which takes a linear form of current wealth level and current liability level. We also analyze the influence of the risk aversion coefficients on the time-consistent portfolio policy and the investment performance via a numerical example.