A simplified inversionless Berlekamp-Massey algorithm for binary BCH codes and circuit implementing the method are disclosed. The circuit includes a first register group, a second register group, a control element, an input element and a processing element. By breaking the completeness of math structure of the existing simplified inversionless Berlekamp-Massey algorithm, the amount of registers used can be reduced by two compared with conventional algorithm. Hardware complexity and operation time can be reduced.