The paper develops a new numerical method to calculate the transmission coefficient for one kind of potential barrier with even parity. In this method

the scattering states and the standing states of Schrodinger equation are connected. Therefore

the transmission coefficients and phases for wave functions with even and odd parities can be solved for such kind of barriers where those quantities have no analytical expressions. As examples

we solve the transmission coefficients and phases for threetyped barriers which clearly display the properties of particles scattered by the barriers.