A valve driving device comprising: a tappet assembly 3 adapted to slide in a tappet guide hole 4 to drive a valve 5 and including a high-speed center tappet 31 and low-speed side tappet 32; and a high-speed center cam 21 and a low-speed side cam 22 (23) provided corresponding to the center tappet 31 and the side tappet 32. A depression 21 a is formed which is depressed from a base circle to roughly the same profile as a shaft section of the camshaft 2 so that the cam portion over a predetermined angle range where a cam nose section is not formed in the centrally located center cam 21 is smaller than the base circles of the outside located side cams 22 (23) in profile.