Processes driven by unsteady reconnection can efficiently accelerate particles in many astrophysical plasmas. An example is the reconnection jet fronts in an outflow region. We present evidence of suprathermal ion acceleration between two consecutive reconnection jet fronts observed by the Magnetospheric Multiscale mission in the terrestrial magnetotail. An earthward propagating jet is approached by a second faster jet. Between the jets, the thermal ions are mostly perpendicular to magnetic field, are trapped, and are gradually accelerated in the parallel direction up to 150 keV. Observations suggest that ions are predominantly accelerated by a Fermi-like mechanism in the contracting magnetic bottle formed between the two jet fronts. The ion acceleration mechanism is presumably efficient in other environments where jet fronts produced by variable rates of reconnection are common and where the interaction of multiple jet fronts can also develop a turbulent environment, e.g., in stellar and solar eruptions.