Grover’s quantum search algorithm is one of the most widely studied and has produced results in some search applications faster than their classical counterpart by a square-root. This paper modifies Grover’s algorithm to solve nonlinear equations over Galois Finite field GF(q) in O(2^nm) iteration, while the best classical general solution takes O(2^nm) iteration. The modification is done by using a register for each variable and represent it by n qubits. The paper also introduces the implementation of the suggested algorithm by using the simulator QCL 5.1.