Two-dimensional Hubbard model with both nearest- and next-nearest-neighbor transfers is studied. A singularity in the charge susceptibility at the Mott transition point delta-->0 is observed, leading to the anomaly of the charge mass m(c)* in the form m(c)* is-proportional-to Absolute value of delta-1, where delta is the doping concentration. The singularity is similar to that in the case without the next-nearest-neighbor transfer. This indicates that the singularity in the charge mass is a universal nature of this model, irrespective of its band structure.