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Generalized function projective lag synchronization(GFPLS) is characterized by the output of the drive system proportionally lagging behind the output of the response system and ratio of the two systems is desired function scaling matrix. In this paper, GFPLS between different chaotic systems with uncertain parameters, i.e. GFPLS between Chen and Lorenz chaotic system is studied by applying an adaptive control method. Based on Lyapunov stability theory, the adaptive controllers and corresponding parameter update rules are constructed to make the states of two diverse chaotic systems asymptotically synchronize up to the desired scaling matrix and to estimate the uncertain parameters. The numerical simulations are provided to show the effective and robustness of the results.