We describe a hill-climbing algorithm that constructs high-girth quasi-cyclic low-density parity check (QC-LDPC) codes. Given a desired girth, the algorithm can find QC-LDPC codes of shorter block-length in much less time compared with the previously proposed ldquoguess-and-testrdquo algorithm. An analysis is also provided to explain when guess-and-test would be expected to perform well or badly.