Multiple-input multiple-output (MIMO) systems play a great role in improving performance of wireless communication system and are commonly used to ensure high bit-rate transmission. Space-time block codes (STBC) are a remarkable modulation scheme discovered recently for the multiple antenna wireless channel. They have an elegant mathematical solution for providing full diversity over the coherent, flat-fading channel. In this paper, a method for approximating the probability distribution of sum of independent and identical Weibull random variables is adopted to derive a tight analytical expressions for various performance criteria of STBC's coding operating under identical and independent Weibull fading channels (WFC). The proposed Analytical expressions are given in terms of simple, gamma and Fox-H functions. These expressions demonstrate the best fit to simulation results using Monte-Carlo simulation and other statistical methods.