We have studied the path integral solution of a system of particle moving i
n a certain class of noncentral potential without using the Kustannheimo-St
iefel transformation. The Hamiltonian of the system has been converted to a
separable Hamiltonian of Liouville type in parabolic coordinates and has f
urther reduced to a Hamiltonian corresponding to two two-dimensional simple
harmonic oscillators. The energy spectrum for this system is calculated an
alytically. The Hartmann ring-shaped potential and compound Coulomb plus th
e Aharanov-Bohm potential have also been studied as special cases.