In this paper a Multi-input-Multi-output (MIMO)-Proportional-Integral-Derivative (PID) control design method via sub-optimal solution of Linear Quadratic Differential Games (LQDG) for Load frequency Control (LFC) of a 2-area interconnected power system is proposed. The main motivation behind the proposed centralised LFC design scheme is to solve multi-objective optimization problem that can accomplish improvement in transient response & disturbance rejection simultaneously. The proposed iterative optimization algorithm in Linear matrix Inequality (LMI) framework yields appropriate sub-optimal PID gains. A 2-area LFC problem is solved using the proposed design and comparative results suggests that the proposed design can significantly attenuate the load disturbances as well as provide improved transient response specifications.