The spin-splitting energies in strained bulk wurtzite aluminum nitride (AlN) are studied using the linear combination of atomic orbital method. It is found that strain and crystal field induce not only a linear-k (£\wz ) but also two cubic-k terms (£^¡¦and £f¡¦ ) in the two-band k¡Dp Hamiltonian Hso=(£\wz-£^¡¦k2//+£f¡¦k2z)(£mxky-£mykx)+H0so, where H0so=(-£^0k2//+£f0k2z)(£mxky-£mykx) is for ideal wurtzite and generates a cone-shaped minimum-spin-splitting (MSS) surface. As biaxial strain increases, the shape of the MSS surface changes from a hexagonal hyperboloid of two sheets in unstrained AlN to a hexagonal cone, and eventually becomes a hyperboloid of one sheet. The spin-splitting energies of first conduction band for A-plane and M-plane wurtzite are calculated by the sp3 linear combination of atomic orbital (LCAO). The results show the spin-splitting energies are dominated by linear-k term but contribution of cubic-k terms can not be neglected for larger k//. The parameter of linear-k and cubic-k terms are evaluated from the LCAO calculated spin-splitting energies fitting to two band k¡Ep model as increasing well width. The coefficients of linear-k and cubic-k terms decrease.