In previous work, we have developed a cost-effective small-animal SPECT imaging system by adding a multi-pinhole cylinder collimator into an animal PET scanner. To achieve high-quality reconstructed SPECT image, accurate geometrical calibration of the collimator is critical, The pinhole position in PET -scanner's coordinate system (PSC) could be factorized into two parts: pinhole position in collimator's coordinate system (fixed, only need one measurement) and collimator position in PSC (would vary after times of use after times of use). In this paper, we propose a novel geometrical calibration method for the second part based on the coincidental beta-gamma events of LYSO background radiation of the PET scanner. To obtain sufficient conditions for describing the collimator in PSC, a mark ball was added to one end of the collimator and imaged with collimator by LYSO background radiation simultaneously. With the reconstructed image of the collimator and the add-on mark ball, the axis of the collimator and the center of the mark ball were derived using least-squares fitting and centroid calculation, individually. Monte-Carlo simulation studies with five groups of different positions of collimator were implemented and geometrical parameters were calibrated. The proposed method was implied on a real system. Both simulation and experiment studies show that the proposed method could achieve high accuracy for parameter calibration. In conclusion, it is a practical and efficient way to perform SPECT collimator calibration by using PET scanner's LYSO background radiation in the studied PET/SPECT system.