The vibration caused by incipient fault is the main factor affecting the accuracy of cam-driven absolute gravimeter. An incipient fault diagnosis method for cam-driven absolute gravimeter is proposed with the modified ensemble empirical mode decomposition （MEEMD）， multi-scale permutation entropy （MPE） and energy entropy， based on the incipient fault features of smaller amplitude， weak fault characteristics and hard-to-find in the noise. After the adaptive decomposition of the vibration signal of the cam-driven absolute gravimeter under different working conditions， the effective intrinsic mode functions （IMF） are selected， and the multi-scale permutation entropy and energy entropy are extracted， as the sensitive features in vibration data. Furthermore， the extracted multi-dimensional vector matrix is loaded into the support vector machine （SVM） whose kernel function is the radial basis function （RBF）， and the accurate incipient fault diagnosis for cam-driven absolute gravimeter is realized based on data. Experimental results show that the proposed method can effectively diagnose various incipient faults for cam-driven absolute gravimeter， and the accuracy of fault diagnosis reaches up to 97.1%. This method solves the problem of low measurement precision in cam-driven absolute gravimeter due to incipient fault， and the incipient fault can be quickly and accurately traced. Meanwhile， it can realize the fast tracing and accurate positioning of the incipient fault for the gravimeter， and has a good prospect for engineering application.