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The capacity of multiple input multiple output (MIMO) system over wireless channels has been investigated analytically and by simulation over different types of wireless fading channels, such as Rayleigh and Nakagami-m fading channels. The capacity of MIMO system over Weibull fading channels has not been considered in the literature before because of the complexity in obtaining closed form expressions for either the probability of outage capacity or the average capacity. In this paper, finite mixture (FM) with expectation-maximization (EM) algorithm is utilized to derive simple approximate expression for the probability density function (pdf) of the capacity distribution over identically independent distributed (iid) Weibull fading channels. This approximation converts the complicated capacity distribution to a simple weighted sum of univariate normal distributions with appropriate weighting coefficients, means, and variances for a predefined system model and channel statistics. The resultant approximation simplifies the mathematical analysis of the average capacity and the outage capacity in terms of well known Q-functions.