This paper considers a robust optimal investment problem for an ambiguity-averse asset-liability manager under the mean-variance criterion in the presence of stochastic volatility. The manager has access to a risk-free (bank account) and a risky asset (stock) in a financial market. Specifically, the stock price is driven by the state-of-the-art 4/2 stochastic volatility model, which recovers the Heston model and 3/2 model, as exceptional cases. By applying the stochastic dynamic programming approach and solving the corresponding Hamilton-Jacobi-Bellman-Isaacs equation, closed-form expressions for the robust optimal strategy and optimal value function are derived. Technical conditions are determined for the verification theorem and well-defined solutions. Moreover, we provide explicit results for two special cases of our model, the ambiguity-neutral manager case and the case without random liabilities. Finally, some numerical examples are presented to illustrate the effects of model parameters on the robust optimal control and optimal value function (efficient frontier). The numerical examples show that the ambiguity aversion levels about the risky asset price and its volatility have different impacts on the amount of wealth invested in the risky asset and on the efficient frontier.