Abstract: In the paper,modified function projective lag synchronization (MFPLS) of a class of chaotic systems of which the drive system and response system are all subjected to unknown external disturbance was investigated,and a general theorem of MFPLS was introduced．Based on Lyapunov stability theorem and adaptive control method,two different res-ponse systems were given,and adaptive controller and disturbance controlling strength update law were constituted.MFPLS of chaotic system was achieved under the condition of unknown system uncertain disturbances,and disturbance controlling strength could also be estimated automatically．Finally,numerical simulation results of a hyperchaotic system verify the validity,effectiveness and robustness of our theoretical results．The designed controller is simple and practical,and has broad application in secure communication and other fields.

Key words: Chaotic system,Modified function projective lag synchronization,Disturbance controlling strength