We proposed a two-layer scheme of Deoxyribonucleic acid (DNA) based computation, DNA-01MKP, to solve the typical NP-hard combinatorial optimization problem, 0-1 multidimensional knapsack problem (0-1 MKP). DNA-01MKP consists of two layers of procedures: (1) translation of the problem equations to strands and (2) solution of problems. For layer 1, we designed flexible well-formatted strands to represent the problem equations; for layer 2, we constructed the DNA algorithms to solve the 0-1 MKP. Our results revealed that this molecular computation scheme is able to solve the complicated operational problem with a reasonable time complexity of O(n×k), though it needs further experimental verification in the future. By adjusting the DNA-based procedures, the scheme may be used to resolve different NP-hard problems.