Abstract: An algorithm called NNDMHD for the two-dimensional, three-component, eight-variable and time-dependent magnetohydrodynamic (MHD) conservative equations is proposed. It reduces Lorentz force error caused by numerical magnetic field divergence's non-zero error in a method of dividing magnetic field into two parts, a potential one invariant of time and a non-potential one varying with time. Then, NNDMHD could be developed from the Non-oscillatory, Non-free parameter Difference scheme (NND), which is very effective in numerical simulation of gas-dynamical transonic flow. At first, numerical tests on NNDMHD are carried out on a typical one-dimensional Riemann case and a two-dimensional Orszag-Tang example. The good numerical results agree with those of references and exhibit no non-physical oscillation near discontinuities. Then, example of solar wind flow in a helmet magnetic field structure being axisymmetric in meridian plane is taken for NNDMHD numerical test. In this example, although physical variables vary in a large scale (-10-4) in radial direction, NNDMHD can still reduce Lorentz force error caused by numerical magnetic field divergence's non-zero error. The numerical result in this example shows that: although the grid mesh is coarser four times than that of usual one, NNDMHD can still keep stable in computation for final steady state result.