The forward stimulated Brillouin scattering based fast light in small-core photonic crystal fibers is theoretically investigated. Three-wave coupled wave equations of forward stimulated Brillouin scattering in frequency domain were derived to calculate the group refractive index and gain coefficient in small-core photonic crystal fibers by Fourier transformation, then optical and acoustic field distribution, advancement and broadening factor of signal pulses induced by forward stimulated Brillouin scattering were simulated by the finite element method. Tight confinement of the optical fundamental mode and acoustic modes strengthens nonlinear interaction in the small-core photonic crystal fibers and results in strong SBS and large advancement of time. The time advancement grows nonlinearly with the transmission distance of signal light increasing, and the signal pulses are compressed. The pulse broadening factor gradually levels off with the growth of the initial pulse width. The time advancement of 21.76 ns and pulse broadening factor of 0.77 are evaluated at the transmission distance of 70 m, the initial pulse width of 200 ns and the pumping pulse power of 600 mW.