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In this paper, we propose an effective and efficient searching method for constructing quasi-cyclic low-density parity-check (QC-LDPC) codes with a desired girth g. We begin with an arbitrary QC-LDPC code with girth-4 and we evaluate only the number of cycles with length 4. When all the cycles with length 4 are removed by adjusting the elements of the QC-LDPC code, we form a QC-LDPC code with girth-6. Subsequently, we consider only the numbers of cycles with length 4 and length 6. In general, knowing that the current QC-LDPC code has a girth of g', we only consider the numbers of cycles with length up to g' even though g' may be smaller than the desired girth g. By using an adaptive cost function, which is defined as the number of cycles of length g', in the optimization/searching process, we are able to reduce the computational effort tremendously compared with Wang's searching algorithm . Consequently, our proposed method can generate QC-LDPC codes with the desired girth much more efficiently.