In this paper, a numerical and experimental investigation is conducted on a novel pneumatic-drive asymmetric Gifford-McMahon cycle cryorefrigerator (GMCR). In the pneumatic-drive asymmetric Gifford-McMahon cycle cryorefrigerator, the duration of the assistance space exhaust process is kept higher than that of the assistance space intake process. Therefore, the displacer moves faster near the lower dead center (LDC) and slower near the upper dead center (UDC) inside the expander cylinder. The numerical model solves the governing equations of the refrigerant and dynamics of free-floating displacer iteratively to illustrate the refrigeration mechanism. Additionally, the model computes the performance parameters of the cryorefrigerator like refrigerating capacity and specific refrigerating capacity. By adopting the numerical model, the impact of the loitering time (LT) on the thermodynamic processes is elaborated. It is perceived that both refrigerating capacity and specific refrigerating capacity reduces with an increase in the loitering time. The experimental cooling characteristics are studied for different values of discharge to suction pressure ratios of helium compressor.