The parity-violating nuclear anapole moment effect can be used as a tool to test nuclear models and gain deep understanding of nuclear structure. Diatomic molecules such as BeCl are considered as good candidates in search for the nuclear anapole moment effect, because such molecules have close-lying molecular levels with opposite parity, where degeneracy can very easily occur in external fields, leading to a dramatic amplification of the tiny parity-violating effect. In order to interpret the results of precision measurements effectively, a parity-violating interaction parameter $W_A$, which depends on molecular structure, needs to be calculated with high-accuracy. In this work, the calculations of the $W_A$ parameter for the Be atom in BeCl are carried out with various electron correlation approaches such as the open-shell single determinant average-of-configuration Dirac-Hartree-Fock (DHF), the relativistic density functional theory (DFT), the second-order M\o{}ller-Plesset method (MP2), the relativistic coupled cluster method with single, double, and perturbative triple excitation, namely CCSD and CCSD(T). The influence of electron correlations on the calculated $W_A$ parameter is investigated and discussed.