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This paper presents a hybrid decoding algorithm for low-density parity-check (LDPC) codes based on the interior point method with barrier function for linear programming (LP) decoding introduced by Wadayama . First, an efficient implementation of Wadayama's algorithm is presented. The main idea behind the modification is to approximate the barrier function for the fundamental polytope defining the code so that it contains only one linear constraint for each of the parity-check constraints. A two-stage hybrid decoding which combines the interior point decoding and a low-complexity decoding algorithm for LDPC codes is then proposed. Simulation results show that the approximations introduced in the proposed algorithms do not result in any performance degradation, while considerably reducing the decoding complexity and latency.