The present article concentrates on the propagation of generalized surface acoustic waves in a composite struc- ture consisting of piezoelectric and non-piezoelectric semiconductor media. The mathematical model of the problem is depicted by a set of partial differential equations of motion, Gauss equation in piezoelectric and elec- tron diffusion equation in semiconductor along with boundary conditions to be satisfied at the interface. The secular equation that governs the propagation of surface waves has been derived in compact form after obtaining the formal solution. The analytic expressions for displacements, stresses, piezoelectric potential and electron concentration during the surface wave propagation at the interface have also been obtained. The numerical solu- tion of the secular equation is carried out for the cadmium selenide and silicon composite by employing fixed point functional iteration numerical method along with irreducible Cardano method. The computer simulated results with the help of MATLAB software in respect of dispersion curves, attenuation coefficient, displace- ments, stresses, carrier concentration and piezoelectric potential are presented graphically. This work may be useful in surface acoustic wave (SAW) devices and electronic industry.