Digital modulation is a process that impresses a digital symbol on to a signal suitable for transmission on a wired or wireless medium in order to receive that signal at receiving end correctly with out any loss of information. Quadratic phase shift keying (QPSK) modulation technique is the most widely used modulation scheme in modern digital communication system; it provides high performance on bandwidth efficiency and bit error rate. In this paper the complete model of Quadrature Phase Shift Keying (QPSK) modulator and demodulator has been developed. The model has been simulated in Matlab using Simulink. Complete results are tested and verified. In final hardware design and implementation of QPSK for Wireless Modem has been proposed. QPSK modulation has various applications particularly in the design of wireless modem, cellular CDMA communication.