The chiral bag plus skyrmion hybrid model is studied as a model for nucleons. The hybrid model is solved numerically, where great care has been taken to remove the divergence in the boundary condition at the chiral bag surface for the nonlinear differential equation of the skyrmion. The numerical results for the nucleon energy turn out to be finite for all bag radii, differing from the case of the linearized chiral model. With a suitable choice of the bag parameter (volume term), the nucleon mass, radius and the axial vector coupling constant g A come out to be very promising.