The linear combinations of harmonic oscillator wave functions (LCWV) method is proposed to solve the Sch odinger equation, for a particle of a mass µ moving in a one dimensional double-well potential field, in which, the energy barrier has a gauss-ian shape. The general double well potential, whether symmetric or not, is constructed from appropriate combinations of Morse-like potentials and a Gaussian function and the problem is solved variationally, using as trial functions, linear combinations of har-monic oscillator wave functions (LCWV) centered at the two minima. The relevant matrix elements are calculated using the Harmonic Oscillator Tensor (HOT) technique. A generalization to multiple well problems is also advanced.