An analysis is performed numerically to study the unsteady free convection heat and mass transfer flow past a semi-infinite vertical flat plate by using finite difference method. First, thermal boundary layer equations have been derived from the Navier-Stokes equation and concentration equation by boundary layer technique. Second, some non-dimensional variable has been introduced to make these equations dimensionless. Then Finite difference method is used to solve these equations. The solution of heat and mass transfer flow is studied examining the velocity, temperature and concentration distribution. The effects on the velocity profiles, temperature profiles and concentration profiles for various parameters have been separately discussed and shown graphically.