This paper considers the problem of recovering low‐rank matrices which are heavily corrupted by outliers or large errors. To improve the robustness of existing recovery methods, the problem is solved by formulating it as a generalized nonsmooth nonconvex minimization functional via exploiting the Schatten p‐norm (0  <  p  ≤ 1) and Lq(0  <  q  ≤ 1) seminorm. Two numerical algorithms are provided based on the augmented Lagrange multiplier (ALM) and accelerated proximal gradient (APG) methods as well as efficient root‐finder strategies. Experimental results demonstrate that the proposed generalized approach is more inclusive and effective compared with state‐of‐the‐art methods, either convex or nonconvex.