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We present the calculation of anomalous muonium in silicon which has been extensively studied but there still remains unresolved problems in the first-principles calculations. We perform calculations using spin-polarized density functional theory within the general gradient approximation or the local density approximation. We check the size effect of supercells and find that we need to use large sizes of supercells to obtain reliable results. Some quantitative disagreement between the experimental and theoretical values in previous studies may be due to the use of insufficient sizes of supercells. We clarify that the negative Fermi contact interaction constant (FCIC) is induced by the electron correlation effect. By using the Hubbard model, we find that the FCIC is zero when we neglect the correlation effect and the negative value of the FCIC is induced by the correlation effect.