This paper proposes improved combined step-size sign subband adaptive filter (ICSS-SSAF) algorithms with variable mixing factors robust to non-Gaussian noises such as impulsive noise. The CSS scheme is adopted to resolve a trade-off problem of step size in the SSAF, combining two adaptive filters with a large step size for a fast convergence rate and a small step size for low steady-state misalignment. Variable mixing factors (VMFs), whose values are changed at every iteration, are introduced to combine the two adaptive filters. To design the VMFs, a modified sigmoidal or arctangent function is employed. They are updated indirectly to minimize the power of approximated system output error, unlike the conventional algorithm using the 1 norm of the error vector composed of error signals divided by subbands. The recursive forms of VMFs are acquired by adopting the gradient method. The simulation results show that the proposed algorithms perform better than conventional algorithms in system identification scenarios.