We have investigated the critical current density for MgB2 films having various crystal orientations prepared by using a hybrid physical-chemical vapor deposition system. An enhancement of the critical current density is clearly presented in MgB2 films with an a-axis or a b-axis orientation rather than a c-axis orientation. X-ray diffraction patterns reveal a suppression of c-axis orientations while a (100) orientation becomes dominant, and the surface morphology of the a-axis-oriented film shows that the orientation of the c-axis-oriented MgB2 grains parallel to the plane of the substrate. As the a-axis orientation becomes more dominant in the MgB2 films, the field performance of the critical current density clearly becomes better. These results suggest that the synthesis of MgB2 with high ab-plane orientations is one of the keys to enhancing the critical current density in MgB2.