Entanglement is an important resource in quantum measurement and quantum information. As a key apparatus of generating entanglement, a non-degenerate optical parametric oscillator (NOPO) can directly output entanglement without any extra operation, unlike the degenerate OPO which needs optical beam coupling of two output squeezings. Most research studies are focusing on the resonant NOPO design, i.e., without detunings, which is the most common cause for generating the best squeezing and entanglement. However, detunings are inevitable and play a crucial role in some experiments such as quantum optomechanics and gravitational wave detection beyond the standard quantum limits with the help of the optical spring effect. NOPO could be used in these experiments to further increase the corresponding sensitivity. Therefore, in this paper, we investigate the effect of detunings on the entanglement degree in the NOPO. Considering the detunings of the pump, signal and idler fields, the quantum Langevin equations are given. Then the stationary solutions for both below and above the threshold of the pump power are obtained and analyzed. The monostable solutions, bistable solutions and unstable solutions are all analyzed. The bipartite entanglement noise spectra of the signal and idler beams are obtained. Analytical solutions below the threshold and numerical solutions above the threshold are both given, and the corresponding results are plotted in 2D/3D. The results show that, the detunings degrade the entanglement degree for most cases, especially at zero frequency or low frequencies. However, the entanglement degree may increase with definite detunings at higher frequencies, i.e., the best entanglement is not at zero frequency, which is the case for NOPO without detunings. Furthermore, the entanglement degree keeps well on a large scale of detunings when the pump detuning and the signal detuning are antisymmetric (one is red detuning, the other blue detuning), much betterthan that of symmetric detuning case, which is an important result from which we can get entanglement of intermediate degree with even large detunings.