T-type three-level (T-3L) power converters are broadly applied in low-voltage and high-current applications, e.g., grid-tied renewable energy generation, micro-energy systems, energy storage, etc. For its control, finite-control-set model predictive control (FCS-MPC) has been recognized as a promising strategy, which is suitable for customized optimization, constrained, and multi-variable systems. However, FCS-MPC depends on model accuracy. Hence, system parameter variations (e.g., DC capacitance, AC side inductance, filter resistance, etc.) will significantly degrade control performance. In this work, we propose a predictive current control technique based on adaptive linear neural network, which evidently improves the robustness of the system against variations of the aforementioned parameters and DC-bus disturbance. The superior performance of the proposed method over classical FCS-MPC is confirmed via simulation and hardware-in-the-loop (HiL) experiment data.