Taking the double arc gear in the national standard GB/T12759-1991 as the analysis object,by using the theory of fuzzy mathematics and reliability optimization design method,considering arc gear transmission allowable stress randomness and fuzziness,taking the fuzzy reliability of arc gear bending modulus strength and contact strength and the modulus,tooth number,helix angle,longitudinal coincidence degree of gear as constraint condition,a minimum volume of arc gear optimization as target,the fuzzy reliability optimum design model of double arc gear is established,and a practical example is given,the results indicate that,the circular gear design with fuzzy reliability optimization design method has better rationality.