The early-type massive binary MQ Cen (P-orb = 3.7 d) has been investigated by means of high-resolution (R similar to 48 000) spectral analysis and multi-band (Johnson BVRI and Stromgren vby) light curve modeling. The physical parameters of the components have been found to be M-1 = 4.26 +/- 0.10 M-circle dot, R-1 = 3.72 +/- 0.05 R-circle dot, T-eff1 = 16 600 +/- 520 K, and M-2 = 5.14 +/- 0.09 M-circle dot, R-2 = 7.32 +/- 0.03 R-circle dot, T-eff2 = 15 000 +/- 500 K for the primary and secondary, respectively. The orbital inclination is i = 87.0 +/- 0.2 deg. The distance to MQ Cen has been derived to be d = 2460 +/- 310 pc which locates it in the Crux OB1 association. However, the age of MQ Cen (similar to 70 Myr) is higher than the one reported for the Crux OB1 association (similar to 6 Myr). The derived masses are implying a spectral type of B5 for the primary and B4 for the secondary component. Nevertheless, the secondary component, which is more massive, appears to be cooler than the primary component: It has completed its lifetime on the main-sequence and it is now positioned at the turn-off point of the giant branch, meanwhile the less massive primary component is still staying on the main-sequence.