The Bin Packing Problem (BPP) is one of the most known combinatorial optimization problems. This problem consists in packing a set of items into a minimum number of bins. There are several variants of this problem; the most basic problem is the one-dimensional bin packing problem (1-BPP). In this paper, we present a new approach based on the GRASP procedure to deal with the1-BPP problem. The first GRASP phase is based on a new random heuristics based on hybridization between First Fit and Best Fit heuristics. The second GRASP phase is based on Tabu search algorithm used for the enhancement of the solutions found in the first phase. The obtained results are very encouraging and show the feasibility and effectiveness of the proposed approach.