To reduce the lower detection limit of 13N gas, we design a γ-γ coincidence measuring instrument including two detectors, a sampling vessel, and a summation and coincidence circuit in this work. The detector uses a 13 cm × 5 cm oversized Bi4Ge3O12  (BGO) scintillator and 172 silicon photomultiplier (SiPM) tubes, which greatly reduce the instrument size while improving the coincidence detection efficiency. The 13N gas coincidence detection efficiency is improved by installing a multilayer metal absorber plate inside the cylindrical sampling vessel. Due to the short half-life of 13N gas, it cannot be stored for a long time; additionally, it is difficult to obtain. It is not possible to directly scale the coincidence detection efficiency of this instrument using a 13N gas source with known activity in engineering projects. Based on the spatial distribution of the relative efficiency of the sampling vessel and the absolute efficiency of the reference point, we use a combination of 22Na solid point source experiments and Monte Carlo simulations to calculate the coincidence detection efficiency of this instrument for 13N gas in this work; the coincidence detection efficiency is approximately 4%, which meets the engineering design requirements.