People with peripheral neuropathy (PN) are at risk of falling. Many people with PN have comorbid cognitive impairment, an independent risk factor of falls, which may further increase the risk of falling in people with PN. However, the negative synergic effect of those factors is yet to be reported. We investigated whether the presence of cognitive impairment exacerbates the risk of falls in people with PN by measuring gait variability during single-task walking and dual-task walking. Forty-four adults with PN were recruited. Based on the Montreal Cognitive Assessment (MoCA) scores, 19 and 25 subjects were cognitively impaired and intact, respectively. We measured coefficients of variation of gait speed, stride length, and stride time using validated body-worn sensors. During single-task walking, no between-group differences were observed (all p > 0.05). During dual-task walking, between-group differences were significant for gait variability for gait speed and stride length (51.4% and 71.1%, respectively; p = 0.014 and 0.011, respectively). MoCA scores were significantly correlated with gait variability for gait speed (r = 0.319, p = 0.035) and stride length (r = 0.367, p = 0.014) during dual-task walking. Our findings suggest that the presence of cognitive impairment exacerbates the risk of falls in people with PN.