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This article demonstrates how the GA approach can be efficiently used to the penalty function based fuzzy goal programming (FGP) formulation of academic personnel planning problems in university management system. In the proposed approach, requirement of total full-time teaching staff and allocation of pay-roll budget to each of academic departments are fuzzily described. The recruitment of minimum number of teaching and non-teaching staff and maintaining of certain ratios of part-time teaching staff and non-teaching staff individually with full-time teaching staff, and a ratio of total number of students with total teaching staff in each department for smooth functioning of the academic activities of the departments are considered as constraints in the academic planning horizon. In the model formulation of the problem, the concept of penalty functions for measuring the degree of achievement of membership goals in different ranges for the defined fuzzy goals and thereby arriving at a satisfactory decision is considered. In the solution process, an GA scheme is employed in an iterative manner to achieve the fuzzy goals on the basis of their assigned priorities in the decision making environment. A case example of the University of Kalyani, West Bengal (W.B), India is considered to illustrate the potential use of the approach.