The Charcot-Marie-Tooth disease 2F (CMT2F) and distal hereditary motor neuropathy 2B (dHMN2B) are caused by autosomal dominantly inherited mutations of the heat shock 27 kDa protein 1 (HSPB1) gene and there are no specific therapies available yet. Here, we assessed the potential therapeutic effect of HDAC6 inhibitors on peripheral neuropathy with HSPB1 mutation using in vitro model of motor neurons derived from induced pluripotent stem cells (iPSCs) of CMT2F and dHMN2B patients. The absolute velocity of mitochondrial movements and the percentage of moving mitochondria in axons were lower both in CMT2F-motor neurons and in dHMN2B-motor neurons than those in controls, and the severity of the defective mitochondrial movement was different between the two disease models. CMT2F-motor neurons and dHMN2B-motor neurons also showed reduced α-tubulin acetylation compared with controls. The newly developed HDAC6 inhibitors, CHEMICAL X4 and CHEMICAL X9, increased acetylation of α-tubulin and reversed axonal movement defects of mitochondria in CMT2F-motor neurons and dHMN2B-motor neurons. Our results suggest that the neurons derived from patient-specific iPSCs can be used in drug screening including HDAC6 inhibitors targeting peripheral neuropathy.