Behavioral and neuroimaging studies have provided evidence that reading is strongly left lateralized, and the degree of this pattern of functional lateralization can be indicative of reading competence. However, it remains unclear whether functional lateralization differs between the first (L1) and second (L2) languages in bilingual L2 readers. This question is particularly important when the particular script, or orthography, learned by the L2 readers is markedly different from their L1 script. In this study, we quantified functional lateralization in brain regions involved in visual word recognition for participants' L1 and L2 scripts, with a particular focus on the effects of L1-L2 script differences in the visual complexity and orthographic depth of the script. Two different groups of late L2 learners participated in an fMRI experiment using a visual one-back matching task: L1 readers of Japanese who learnt to read alphabetic English and L1 readers of English who learnt to read both Japanese syllabic Kana and logographic Kanji. The results showed weaker leftward lateralization in the posterior lateral occipital complex (pLOC) for logographic Kanji compared with syllabic and alphabetic scripts in both L1 and L2 readers of Kanji. When both L1 and L2 scripts were non-logographic, where symbols are mapped onto sounds, functional lateralization did not significantly differ between L1 and L2 scripts in any region, in any group. Our findings indicate that weaker leftward lateralization for logographic reading reflects greater requirement of the right hemisphere for processing visually complex logographic Kanji symbols, irrespective of whether Kanji is the readers' L1 or L2, rather than characterizing additional cognitive efforts of L2 readers. Finally, brain-behavior analysis revealed that functional lateralization for L2 visual word processing predicted L2 reading competency.