Using a three-dimensional compressible MHD code, I have numerically studied the asymmetric magnetic reconnection at the dayside magnetopause where (1) the magnetic field is higher on magnetospheric side, and where (2) the density is higher on magnetosheath side. Reconnection is caused by applying a localized resistivity in the center of the current sheet, which is dependent on the y- and z-component to give three-dimensional effect. Sudden onset of reconnection causes the development of a bulge in the current layer. But at xy-plane, its shape and velocity are different from the two-dimensional model. Even without any initial z-component of magnetic field, the field lines are found to be tilted. When the bulge has moved far enough from the reconnection site, steady reconnection proceeds at the X-line. Quasi-steady state of the reconnection has elongated field lines along the magnetopause. Also the erosion effects are weak. At xy plane, discontinuities are similar to the two dimensional model, but the variation of z value has changed the discontinuity type. It is found that the greater heating happens on the magnetospheric side discontinuity in both cases.