The effect of magnetic field h on the anisotropic susceptibility in a spin S=12 anisotropic three-dimensional Heisenberg ferromagnet, is studied by the double-time Green's function method within Tyablikov approximation. The position T m and height χ(T m ) of the maxima of both longitudinal and transverse susceptibilities are all fitted satisfactory to power laws: T m −T 0 ∝h γ , and χ(T m )∝h −β . Here the powers (γ and β) are not critical exponents close to the critical temperature T c , and T 0 =T c , 0 for longitudinal and transverse susceptibilities, respectively. The powers (γ and β) are found to be strongly dependent on the anisotropy, which do not support the mean-field power law with exponent to be 23. The origin of difference between the behaviors of the longitudinal and transverse susceptibility is discussed. Besides the power laws, more interesting is that in the weak anisotropy case, the position T m ⊥ of the maximum transverse susceptibility displays anomalous phenomena under different magnetic field h.