In this letter, an NB RCP LDPC (Non-Binary Rate-Compatible-Punctured Low Density Parity Check) code has been designed over the extended Galois Field. The designed code enables us to change the code rate easily by properly puncturing the appropriate symbols from the LDPC mother code. The designed NB RCP LDPC code has been applied to the Type II HARQ (Hybrid Automatic Repeat reQuest) scheme using OFDM (Orthogonal Frequency Division Multiplexing) modulation. The throughput characteristics of the proposed HARQ scheme are evaluated through computation simulation.