Bipolar depression is commonly accompanied by cognitive impairments. Transcranial direct current stimulation (tDCS) is emerging as a novel non-invasive treatment for bipolar depression. Given the portability and safety of tDCS, we developed a home-based protocol with real-time supervision. Our aim was to assess the cognitive effects of a course of tDCS treatment in bipolar depression. 44 participants (31 women, mean age 47.27 years, SD 12.89) with bipolar depression of at least a moderate severity received 21 sessions of home-based tDCS over 6 weeks in an open-label design. The stimulation protocol involved 2 mA in a bilateral frontal montage (F3 anode, F4 cathode) for 30 min per session. Cognitive assessments were conducted at baseline and after the course of treatment: Rey Auditory Verbal Learning Test (RAVLT) to assess verbal learning and memory and Symbol Digit Modalities Test (SDMT) to assess psychomotor processing speed and visuospatial attention. 93.18% (n = 41) completed RAVLT and 59.09% of participants (n = 26) completed SDMT. A significant improvement was observed in RAVLT verbal learning score post-treatment (p = 0.002), which was not maintained following adjustment for improvement in depressive symptoms. In summary, a course of home-based tDCS in bipolar depression was associated with an improvement in verbal learning, which appeared to be related to improvement in depressive symptoms. These findings suggest potential benefits of tDCS for addressing cognitive impairments in bipolar depression, which can be investigated further in a sham-controlled design.