The existing distributed Newton algorithm for network utility maximization cannot be directly applied into the wireless ad hoc networks, as it does not consider the wireless link capacity variation and transmission power consumption. Regarding these, a new joint network utility maximization problem is formulated to optimize the wireless ad hoc network resource utility. The distributed Newton algorithm is implemented to solve for the dual variables and Newton directions by using the local information at each session source and link, respectively. Furthermore, a new iterative method is proposed to improve the convergence rate of the existing matrix-splitting method. Simulation results validate the efficiency and efficacy of the proposed distributed Newton algorithm for wireless ad hoc network utility maximization.