A new type of mass damper is presented for passive seismic response control of spatial structures subjected to bi-directional ground motions. The mass damper consists of a three-degree-of-freedom compliant mechanism with a mass, three springs and a viscous damper. By utilizing the flexibility of springs, the movement of the mass is amplified in two directions and the vibration energy of the mass is absorbed by the viscous damper. The candidate parameters of the mass damper are first searched globally using a random selection of the discretized parameter values by carrying out a series of dynamic response analyses. The parameters are further optimized using a heuristic approach called tabu search. The characteristics and the effectiveness of the mass damper are discussed in comparison to the conventional tuned mass damper that has single-degree-of-freedom.