For a structure with implicit performance function structure and less sample data, it is difficult to obtain accurate probability distribution parameters by traditional statistical analysis methods. To address the issue, the probability distribution parameters of samples are often regarded as fuzzy numbers. In this paper, a novel fuzzy reliability analysis method based on support vector machine is proposed. Firstly, the fuzzy variable is converted into an equivalent random variable, and the equivalent mean and equivalent standard deviation are calculated. Secondly, the support vector regression machine with excellent small sample learning ability is used to train the sample data. Subsequently, and the performance function is approximated. Finally, the Monte Carlo method is used to obtain fuzzy reliability. Numerical examples are investigated to demonstrate the effectiveness of the proposed method, which provides a feasible way for fuzzy reliability analysis problems of small sample data.