We present a tunable second-order Polarization Mode Dispersion (SOPMD) module with constant mean first-order differential group delay (DGD). The module consists of a variable DGD line (variable from τminvariable to τmaxvariable), a polarization controller, and a high birefringent (HiBi) fiber segment with a DGD value of τfixed. A Muller transitional matrix has been employed to describe the system. Theoretical calculations predict that after careful calibrations, by tuning the variable DGD line, the module can provide SOPMD values variable from Φ0 to 1/2τ2fixed+Φ0(Φ0 is a constant), while its mean first-order DGD is kept at a constant value of about τfixed. We implemented two of such modules, e.g. module No. 1 and No.2, which have different tuning range of SOPMD and different mean DGD values. For module No. 1, a variable DGD line (variable from 0.68 to 15.00 ps) and a HiBi fiber with a DGD value of about 10.5 ps were used. Module No. 1 demonstrates variable SOPMD values from about 37.0 to 522.0 ps2 with an accuracy of about ±1.0 ps. Module No. 2 demonstrates variable SOPMD values from about 10.0 to 63.0 ps2 with an accuray of about ± 5.0 ps2, while its mean first-order DGD is kept at a ocnstant value of about 10.5 ± 1.0ps. The implications of this tunable Second-order PMD Module on high-speed (≥ 10 Gbit/s) optical communications are discussed.