Interference channel (IC) is a classical model used to characterize the effect of interference for many real-life communication systems. In this paper, we consider a sum rate maximization problem subject to maximum power restriction at each transmitter for a single-input single-output (SISO) IC network. The considered power control problem is typically a nonconvex problem which is hard to solve directly. We propose a solving algorithm for this power control problem based on successive convex approximation (SCA). Specifically, we first reformulate the original nonconvex objective function as the difference of two concave (D.C.) functions near a given point in the feasible region of the solution space. After that, we construct a convex substitute function for the D.C. objective by approximating its second concave function with the one-order Taylor expansion. The problem is further reformulated as an unconstrained problem by transforming the constraints as a barrier function. This unconstrained problem is then solved iteratively using Newton's method. We update the substitute function given the newly obtained solution, near which the one-order Taylor expansion is performed again. This process is then repeated until a smooth point is reached. Simulation results show the effectiveness of the proposed SCA-based power control algorithm.