Braid group is a new considerable public key cryptography platform for the quantum computer ages, but almost all current intractable braid problems used for public key cryptosystems are flawy. The security of a braid public key cryptosystem can’t depend only on the hardness of conjugacy problems. By taking advantage of the non-conjugate transformation and multiple variant equations on braid groups, two intractable problems are proposed, and the hardness of these problems comes from the enlarged amount of variants. A new related public key algorithm and the analysis of its correctness, security, efficiency and parameter choice are subsequently presented. The new algorithm can resist current known attacks, and the ideal to combine some simple problems to a multiple variant difficult one is constructive for designing new public key algorithms.