We have measured the low-temperature specific heat C(T) for polycrystalline MgB 2 prepared by high pressure synthesis. C(T) below 10 K vanishes exponentially, which unambiguously indicates a fully opened superconducting energy gap. However, this gap is found to be too small to account for T c of MgB 2 . Together with the small specific heat jump ΔC/γ n T c = 1.09, scenarios such as anisotropic s-wave or multicomponent order parameter are called for. The magnetic field dependence of γ(H) is neither linear for a fully gapped s-wave superconductor nor H 1/2 for nodal order parameter. It seems that this intriguing behavior of γ(H) is associated with the intrinsic electronic properties other than flux pinning.