We consider a double scaling limit of the plane wave matrix model (PWMM), in which the gravity dual geometry of PWMM reduces to a class of spherical NS5-brane solutions. We identify the form of the scaling limit for the dual geometry of PWMM around a general vacuum and then translate the limit into the field theoretic language. We also show that the limit indeed exists at least in a certain planar 1/4-BPS sector of PWMM by using the localization computation analytically. In addition, we employ the hybrid Monte Carlo method to compute the matrix integral obtained by the localization method, near the parameter region where the supergravity approximation is valid. Our numerical results, which are considered to be the first computation of quantum loop correction to the Lin-Maldacena geometry, suggest that the double scaling limit exists beyond the planar sector.