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We study an evolutionary prisoner's dilemma game on a scale-free network by a modified Fermi updating rule, where each player is assigned an inertia index that controls its learning activity. An interesting finding is that the cooperation level can be significantly improved when the individual inertia is introduced. More importantly, a parameter β is also introduced to control the diversity level of inertia among the individuals. It is found that there exists an optimal value of β leading to the highest cooperation level. The observed results are explained by the feedback mechanism and the characteristic of the Fermi function. Our analysis also reveals that the players with moderate degrees play a critical role in the evolution of the whole system.