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Magnetoresistivity measurements with fine tuning of the field direction on high quality single crystals of the ferromagnetic superconductor UCoGe show anomalous anisotropy of the upper critical field H _c2 . H _c2 for H ∥ b -axis ( H _c2 ^b ) in the orthorhombic crystal structure is strongly enhanced with decreasing temperature with an S-shape and reaches nearly 20 T at 0 K. The temperature dependence of H _c2 ^a shows upward curvature with a low temperature value exceeding 30 T, while H _c2 ^c at 0 K is very small (∼0.6 T). Contrary to conventional ferromagnets, the decrease of the Curie temperature with increasing field for H ∥ b -axis marked by an enhancement of the effective mass of the conduction electrons appears to be the origin of the S-shaped H _c2 ^b curve. These results indicate that the field-induced ferromagnetic instability or magnetic quantum criticality reinforces superconductivity.