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By using the restricted and complementary relationship of the principle and secondary indexes, providing the description of the compound quantification of the fuzzy number, and analyzing the essential characteristic of fuzzy decision, we propose a kind of fuzzy genetic algorithm based on the principle index (PO-FGA for short) to deal with the fuzzy optimization and programming problems with fuzzy coefficients, fuzzy variables and fuzzy constraints. The concrete solution method is presented in accordance with the strategy of the unconditional penality transformation with conditional constrains. Then consider its convergence by using Markov chain theory and analyze its performance through two examples. All these indicate that this kind of algorithm is of faster speed of convergence, smaller number of iterations, has lower chances of trapping into the state of premature convergence and can be widely used in many problems of optimization.