In this paper, a fast and efficient signal reconstruction algorithm for solving the basis pursuit (BP) problem in compressed sensing (CS) is proposed. This fast linearized Bregman method (FLBM), which is inspired by the fast method of Beck et al., is based on the fact that the linearized Bregman method (LBM) is equivalent to a gradient descent method when applied to a certain formulation. The LBM requires $O(1/{varepsilon})$ iterations to obtain an ${varepsilon}$-optimal solution while the FLBM reduces this iteration complexity to $O(1/sqrt{varepsilon})$ and requiring almost the same computational effort on each iteration. Our experimental results show that the FLBM can be faster than some other existing signal reconstruction methods.