We consider two types of equations shown below: ax^4+ by^4= cz^4+ dw^4 ax^4+ by^4+ cz^4= dw^4 Condition: product (abcd) not equal to zero Existence of solution for Diophantine equation: ax^4+ by^4= cz^4+ dw^4 & ax^4+ by^4+ cz^4= dw^4, are known if (abcd) is square number& product not equal to zero. So we are curious about whether above equation has a solution if (abcd) is not square number & product not equal to zero. In particular, when does this equation have infinitely many integer solutions? Bremner, A., & Choudhry, A., & Ulas [1] have showed the solution family of the similar equation ( ax^4+ by^4+ cz^4+ dw^4= 0 ) with infinitely many rational points using elliptic curve theory. We show other family of solution of this equation with infinitely many rational points. As a bonus we have considered an interesting case of equation (ax^4+ by^4= az^4+ bw^4) in which the product of the coefficents is a square number, but has been parameterized by using only algebraic methods without taking re-course to elliptic curve theory.