We unveil the existence of a two-particle bound state in the continuum (BIC) in a one-dimensional interacting nonreciprocal lattice with a generalized boundary condition. By applying the Bethe-ansatz method, we can exactly solve the wave function and eigenvalue of the bound state in the continuum band, which enable us to precisely determine the phase diagrams of BIC. Our results demonstrate that the nonreciprocal hopping can delocalize the bound state and thus shrink the region of BIC. By analyzing the wave function, we identify the existence of two types of BICs with different spatial distributions and analytically derive the corresponding threshold values for the breakdown of BICs. The BIC with similar properties is also found to exist in another system with an impurity potential.