The determination of the varying position and shape of magnetopause is one of the important Gordian knots in geophysics and space physics. According to the solar wind-magnetosphere-ionosphere coupling global magnetohydrodynamic (MHD) simulation, and with the maximum electric current criterion, we study the position and shape of the magnetopause under several solar wind dynamic pressure (Dp) and interplanetary magnetic field conditions. The simulation results show that the subsolar position (r0) of the magnetopause is controlled mainly by Dp with the significant decrease of r0 as Dp increases. At a certain Dp, when southword Bz (Bz0) decreases to zero, then shifts to northward (Bz0) and increases, the subsolar position r0 keeps increasing. For all cases studie here, the flare angle () of the magnetopause experiences small changes. This provide an evidence for the structural self-similarity of magnetopause in equatorial plane. Compared with the empirical low-latitude magnetopause model of Shue98, MHD simulation can reproduce the dependence of the subsolar point r0 on Dp, while the saturation effect of r0 varying with Bz in empirical model is represented only with slow solar wind. As to the flare angle , although the difference between MHD simulation and empirical model is less than 2.5, the variation of with Bz in MHD simulations is nonlinear and different from the linear trend in empirical model.