The hydrogen evolution reaction (HER) and the oxygen evolution reaction (OER) have been envisaged on a two-dimensional (2D) boron sheet through electronic structure calculations based on a density functional theory framework. To date, boron sheets are the lightest 2D material and, therefore, exploring the catalytic activity of such a monolayer system would be quite intuitive both from fundamental and application perspectives. We have functionalized the boron sheet (BS) with different elemental dopants like carbon, nitrogen, phosphorous, sulphur, and lithium and determined the adsorption energy for each case while hydrogen and oxygen are on top of the doping site of the boron sheet. The free energy calculated from the individual adsorption energy for each functionalized BS subsequently guides us to predict which case of functionalization serves better for the HER or the OER.