The attractiveness of majority-logic decoding is its simple implementation. However, it provides a modest amount of coding gain. A modified Massey's majority-logic decoding algorithm is proposed to improve error-correcting performance. With hard-decision and soft-decision, the modified algorithm is applied to decode the (30,14) shortened Reed-Muller (RM) code in TETRA as well as syndrome algorithm, Massey's majority-logic algorithm, and Rudolph's majority-logic algorithm. Simulation results show that, the proposed modified algorithm can provide more coding gain than the original Massey's algorithm, the modified scheme has the best performance of error correction among four hard-decision schemes, and the Rudolph's scheme outperforms the other three schemes in the case of soft-decision.