A position tracking for a series of mass-spring-damper system via decentralized control design is proposed. First we derive the dynamical model for each subsystem with interconnections. Under the constraint of the fix points of this model, the reference output to be tracked is chosen. Since this is tracking but not regulation, some constant input should be provided and calculated in advance. Then based on the optimal control technique, the decentralized control design is investigated to guarantee the global exponential stability of the overall system. Computer simulations of a 4-mass interconnected mass-spring-damper system are conducted. From these results, all the states approach their reference values exponentially. This has shown the feasibility of our decentralized control design.