Pairing computations on elliptic curves with odd prime degrees are rarely studied as low efficiency. Recently, Clarisse, Duquesne and Sanders proposed two new curves with odd prime embedding degrees: BW13-P310 and BW19-P286, which are suitable for some special cryptographic schemes. In this paper, we propose efficient methods to compute the optimal ate pairing on this types of curves, instantiated by the BW13-P310 curve. We first extend the technique of lazy reduction into the finite field arithmetic. Then, we present a new method to execute Miller's algorithm. Compared with the standard Miller iteration formulas, the new ones provide a more efficient software implementation of pairing computations. At last, we also give a fast formula to perform the final exponentiation. Our implementation results indicate that it can be computed efficiently, while it is slower than that over the (BLS12-P446) curve at the same security level.