The radial wave function of Schr?dinger equation for the anharmonic oscillator potential V(r)=ar2+br4+cr6 can be written in the form of a product of an exponential function and a polynomial function .The exact energy and wave function of the potential are obtained by using the relation for the coefficient of the polynomial function. In the bound states, the results show that parameters a,b and c in the model potential have to satisfy relevant restraint conditions.