  Using the coordinate transformation method, we solve the one-dimensional
Schr\"{o}dinger equation with position-dependent mass(PDM). The explicit
expressions for the potentials, energy eigenvalues and eigenfunctions of the
systems are given. The eigenfunctions can be expressed in terms of the Jacobi,
Hemite and generalized Laguerre polynomials. All potentials for these solvable
systems have an extra term $V_m$ which produced from the dependence of mass on
the coordinate, compared with that for the systems of constant mass. The
properties of $V_m$ for several mass functions are discussed.
