The invention discloses a hydraulic 
inertia-
capacitance balance tuning vibration damping device. The vibration damping device comprises a protective cylinder. A 
mass block is arranged inside the protective cylinder. Two opposite side faces of the 
mass block are connected with '
inertia-
capacitance-damping' vibration damping units, the other two opposite side faces of the 
mass block are each connected with a positive-negative rigidity parallel-connection unit. Each '
inertia-
capacitance-damping' vibration damping unit comprises two vibration damping cavities, a 
piston rod, a 
piston, a curved tubeand an induction control device, wherein the two vibration damping cavities communicate with each other through the 
curved tube, a power-on coil is wound around the local area of the 
curved tube, andthe power-on coil is connected with the induction control device; the mass block is connected with the pistons located in the vibration damping cavities through the 
piston rods. The two positive-negative rigidity parallel-connection units are located at the two sides of the mass block. Each positive-negative rigidity parallel-connection unit comprises an insulation cylinder, a 
magnet and a U-shaped soft 
steel bar. The mass block is connected with two rigidity rods. The two rigidity rods extend into the two insulation cylinders respectively to be connected with a linkage block. Two sleeved annular magnets are arranged inside each insulation cylinder. The two annular magnets are connected through U-shaped soft steel bars. The linkage blocks are connected with the annular 
magnet located at the inner ring.