This paper reports the results of a numerical investigation in to the two-degree-of-freedom (2-DOF) flow-induced vibration (FIV) of two rigidly coupled tandem cylinders of unequal diameters at a low Reynolds number of 150. Three typical center-to-center spacing ratios of L/D = 1.5, 3.75 and 6.0 are examined in the reduced velocity range of Ur = 3–12. For the rigidly coupled tandem cylinders, three typical flow regimes are observed including extended-body regime, reattachment regime and co-shedding regime. The occurrence of flow regime transition is associated with the spacing ratio (L/D) and the reduced velocity (Ur). Accordingly, the flow regime is illustrated in the L/D–Ur diagram. The hydrodynamic forces of both cylinders are significantly reduced in the extended-body regime, resulting in an excellent suppression of FIV. In contrast, both the hydrodynamic forces and response amplitudes are augmented at L/D = 3.75 and L/D = 6.0 as compared with those at L/D = 1.5. Furthermore, the cross-flow amplitude is even larger than that of an isolated cylinder at Ur ≥ 8 with the associated response frequency deviating from the Strouhal curve. The transition of flow regime affects the phase angle of the upstream cylinder. As a greater lift force exerted on the downstream cylinder and the corresponding phase difference with the vibration displacement is either close to 0° or about 180°, the downstream cylinder dominates the movement of the rigidly coupled cylinders in the majority of an oscillating cycle.