Fano resonances usually arise when a narrow resonance or discrete state and a broad resonance or continuum state are coupled. In this paper, we theoretically and numerically study asymmetric Fano line shape realized in a photonic crystal nanobeam (PCN) side-coupled with a photonic crystal nanobeam cavity (PCNC). Asymmetric transmission profiles with a transmission peak and a transmission valley are obtained for a low index concentrated cavity mode. The transmission valley, associated with the destructive interference, of our PCN-PCNC structures is deeper than that of a waveguide or Fabry-Perot resonator side-coupled with a PCNC structure. Through changing the position of the photonic band gap (PBG) of the PCN, we can utilize the high or low frequency band edge modes and the Fano transmission profiles can be further controlled. The transmission spectra of our PCN-PCNC structures can be well fitted by the Fano resonance formula and agree qualitatively with the prediction made by the temporal coupled mode theory. By using the band edge modes of the PCN as the continuum state instead of a usual broad resonance, we have demonstrated a new way to generate a prominent Fano resonance. Our PCN-PCNC structures are compact and feasible to achieve large-scale high-performance integrated photonic devices, such as optical modulators or switches.