We have demonstrated a widely-tunable femtosecond fiber source between 770-1180 nm enabled by self-phase modulation, and the wide spectral coverage is suitable for most of two-photon fluorescence microscopy applications. Based on femtosecond Yb:fiber laser, we also compared spectral broadening in different dispersion regimes using different photonic crystal fibers. We managed to maximize the self-phase modulated feature from the broadened spectra while avoiding unwanted nonlinear temporal trapping. The optimization of fiber selection and laser input conditions led to a wide tunability down to below 800nm region, which is the most commonly used two-photon excitation wavelength for many intrinsic fluorescent labels in biological tissues. We believe this fiber-based femtosecond source can be a relatively cost-effective and robust solution for most of two-photon fluorescence microscopy applications.