A new parallel algorithm for the knapsack problem is proposed, in which the method of divide and conquer is adopted. Based on an CREW-SIMD machine with shared memory, the proposed algorithm needs O(2^n/4)^1-ε processors, 0≤ε≤1, and Oi>O(2^n/2) memory to find a solution for the n-element knapsack problem in O(2^n/4(2^n/4)^ε) time. The cost of the algorithm is O(2^n/2), which is optimal and an improved result over the past researches. The wrong results in corresponding literatures are also pointed out in this paper.