In recent years, pultruded glass fiber reinforced polymer (PGFRP) composites have been increasingly adopted in civil infrastructures worldwide. Nonetheless, the orthotropic nature and relatively weak shear strength make PGFRP beams suffer from the premature local failure at flange-web junction when subjected to concentrated load. In this regard, this paper conducted a series of three-point bending tests on PGFRP I- and Box-beams so as to investigate their failure mode and strength. In particular, three different I-sections and three different Box-sections were used. The beam span-to-depth ratio of 4 was adopted. The experimental results showed that the local failure of PGFRP beams was induced by combined forces of shear, compression and transverse tension. PGFRP I-beams showed clear linear-elastic behavior with sudden brittle failure, while PGFRP Box-beams showed some extent of pseudo-ductile behavior after reaching the first peak load. In addition, existing design methods were evaluated against experimental results, and over-estimations of design methods were observed.