We study the ground state and low excited states of NH radical by using the CCSD(T) method in the coupled cluster theory and the secondary configuration interaction QCISD(T) method combined with the aug-cc- pv5z basis set. The potential energy functions of the ground and excited states of NH radical were fitted. The spectroscopic constants of the corresponding states of NH radical were calculated based on the potential energy function, and compared with the experimental values, the error was found to be small. By solving the radial Schrödinger equation of the ground and excited states of NH radical, the vibrational energy levels and centrifugal distortion constants of the ground and excited states of NH radical at the rotating quantum number J=0 are obtained.