Submicrometre particles of multiferroic BiMn2O5 are prepared by a hydrothermal method. We demonstrate for the first time that BiMn2O5-multiwalled carbon nanotube (MWCNT) composite can be used as a new active material for positive electrodes of electrochemical supercapacitors (ES). The possibility of fabrication of BiMn2O5–MWCNT composites from colloidal suspensions using Celestine blue dye as a co-dispersant for BiMn2O5 and MWCNT is demonstrated. The composite BiMn2O5–MWCNT electrodes with high mass loading and high active material to current collector mass ratio show a capacitance of 6.0 F cm−2 (540 F cm−3) at a scan rate of 2 mV s−1 and capacitance retention of 75 and 58% at scan rates of 100 and 200 mV s−1, respectively. The new findings pave the way to the fabrication of efficient asymmetric devices, containing BiMn2O5–MWCNT positive electrodes and activated carbon–carbon black (AC–CB) negative electrodes. The asymmetric device shows good capacitive behavior and good cyclic stability in a voltage window of 1.8 V. The analysis of power-energy characteristics indicates that maximum energy density of 13.0 W h L−1 (9.0 W h kg−1) and maximum power density of 3.6 kW L−1 (2.5 kW kg−1) can be achieved.