The transmission coefficient for one-dimensional potential with arbitrary shape is calculated using the recurrence formulae of one-dimensional multi-stepped potentials. Resonance tunneling phenomena are studied with the curves of transmission coefficients varying with the energy of incident particles. In particular, the resonance tunneling phenomena in the semiconductor material GaAlAs/GaAs/GaAlAs are discussed in detail. The calculated results show that the resonance tunneling phenomenon for the potential, which has an arbitrary shape well between double symmetric square barriers could also exist.