The structural, electronic, magnetic and thermodynamic properties of the half-Heusler alloy CoTcSn are determined using FP-LAPW method based on density functional theory (DFT). The exchange-correlation potential is treated with the generalised gradient approximation (GGA) described by Perdew–Burke–Ernzerhof (PBE-GGA),GGA plus band-correlated Hubbard parameter (GGA+$U$) and GGA+$U$ plus Tran–Blaha-modified Becke–Johnson (mBJ-GGA+$U$) approximations. Structural results reveal that CoTcSn is stable in phase (II), the ferromagnetic state. The negative values obtained for the formation and cohesion energies confirm that our compound can be synthesised and stabilised experimentally. Electronic and magnetic properties show the half-metallic character of CoTcSn with indirect band gap in minority spin direction of 0.491 and 1.005 eV, and large half-metallic gap of 0.430 and 0.739 eV using GGA+$U$ and mBJ-GGA+$U$, respectively. Results suggest that CoTcSn is a promising candidate for spintronic devices. The integer total magnetic moment of 2 $\mu$B is in conformity with the Slater–Pauling rule. The thermodynamic properties for the Co-based half-Heusler CoTcSn are also investigated using Debye quasiharmonic model.