Network utility maximization has been widely adopted to allocate the resource of networks. However, it suffers from slow convergence under distributed computational environment. This paper proposes a fast rate control algorithm to maximize network utility for energy harvesting in a wireless sensor network. Energy harvesting and channel bandwidth limits are considered together to formulate as a utility maximization problem. Then, an accelerated distributed gradient method is proposed to solve the problem for energy harvesting. Numerical experiments show that the accelerated method achieves faster convergence to the optimal sampling rate under energy and channel constraints than traditional gradient descent methods.