The search for acid-base bifunctional catalysts has become a hot topic in the preparation of biofuels from renewable resources. In the present work, a series of novel acid-base bifunctional metal-boron catalysts were successfully prepared by a sol-gel method and characterized by XRD, IR, SEM, TEM, TGA, BET, and TPD. Among those bifunctional solid materials, the Ca-B(700) catalyst had the highest density of both acid and base sites and showed excellent catalytic performance in the production of biodiesel from nonedible oils with high acid value. Under the optimal reaction conditions of 20/1 methanol/oil mole ratio and 4 wt % catalyst dosage at 105 °C for 2 h, a high biodiesel yield of 96.0% could be obtained from Jatropha curcas oil in one-pot. In addition, Ca-B(700) was also applicable to producing biodiesel from Firmiana platanifolia L.f. oil in a relatively low acid value, with an almost quantitative yield (98.5%) at 65 °C after 2 h. The Ca-B(700) catalyst had good stability and reusability, which is a promising acid-base bifunctional catalytic material for the preparation of biodiesel.