The third generation wireless personal and mobile communication systems are required to support both high-quality and high data-rate services. However, highspeed transmission over wireless communication links is severely restricted by the wireless environment limitations such as inter-symbol interference, propagation fading, additive noise and co-channel interference. This paper investigates the use of space-time coding for high-speed data transmission, as well as, study the effect of time delay spread on such scheme in multipath fading channels. Using a random variable decomposition technique, we also present an analytical model and obtain an approximate bound of the pair-wise error probability for space-time coded systems over multi-path and time-dispersive fading channels. It is shown that the presence of multipath does not reduce the diversity gain provided by the original design criteria which is adopted to construct specific space-time codes in quasi-static flat fading, but the coding gain decreases due to the effect of multiple paths.