A lattice Boltzmann model for miscible viscous fingering in porous media is proposed. Stable displacement between two fluids with same viscosity is simulated. Good agreement with analytical solution is obtained. Specifically,effects of viscosity contrast and Peclet number are investigated. It shows that great viscosity contrast makes fingers grow faster. As viscosity contrast is given,there exists a critical Peclet number above which tip-splitting happens. Study on transversely averaged concentration profile indicates that mixing length first goes as t^1/2,then shifts into a linear dependence in t.