PKS 1424+240 is a distant very high energy gamma-ray BL Lac object with redshift $z=0.601$. It was found that pure synchrotron self-Compton (SSC) process normally need extreme input parameters (e.g., very low magnetic field intensity and extraordinarily large Doppler factor) to explain its multi-wavelength spectral energy distributions (SEDs). To avoid the extreme model parameters, different models have been proposed (e.g., two-zone SSC model or lepto-hadronic model). In this work, we employ the traditional one-zone leptonic model after including a weak external Compton component to re-explore the simultaneous multi-wavelength SEDs of PKS 1424+240 in both high (2009) and low (2013) states. We find that the input parameters of magnetic field and Doppler factor are roughly consistent with those of other BL Lacs if a weak external photon field from either broad line region (BLR) or the dust torus. However, the required energy density of seed photons from BLR or torus is about 3 orders of magnitude less than that constrained in luminous quasars (e.g., flat-spectrum radio quasars, FSRQs). This result suggests that the BLR/torus in BL Lacs is much weaker than that of luminous FSRQs (but not fully disappear), and the inverse-Compton of external photons from BLR/torus may still play a role even in high synchrotron peaked blazars.