The paper presents an exact solution method based on a new linearization scheme for the 0-1 quadratic knapsack problem, which consists of maximizing a quadratic pseudo-Boolean function with nonnegative coefficients subject to a linear capacity constraint. The linearization proposed offers three possibilities to compute an upper bound for (QKP). The authors have suggested a theoretical and an experimental comparison so as to select the most appropriate method which will be incorporated in a branch-and-bound algorithm. A branch-and-bound procedure is developed including the upper bound, a special feasible solution, and a fixing variables procedure at each node of the search tree. Finally, computational results are reported so as to assess how the upper bound as well as the branch-and-bound behaves.