We demonstrated a fiber-based synchronously pumped optical parametric oscillator (SPOPO) with flexible repetition rates while retaining the cavity length. In contrast to conventional free-space SPOPO, the repetition rate of output signal pulses was solely determined by the repetition rate of the pump source in harmonic, fractional and rational operations. The relevant mechanism relies on synchronous pumping and intrinsic losses in our fiber resonator. The novel scheme enabled us to flexibly tune the repetition rate from 0.5 to 6.0 MHz without altering the resonator configuration. The resulting pulse properties were systematically analyzed at various operation conditions, and particularly showed that a wavelength tuning range of 157 nm was obtained. Such rational harmonic resonance implemented in our SPOPO provides not only a simple yet effective way to tune the repetition rate, but also a feasible approach to narrow down the spectral bandwidth. The presented SPOPO could be useful in nonlinear biomedical imaging by offering a convenient approach to optimize the pulse repetition rate for different biomedical samples with minimum photodamage.