In the present work, the structural, magnetic properties and barocaloric effects of the (MnCoGe)0.96-(CuCoSn)0.04 alloy were investigated. At an ultra-low pressure of 0.3 kbar, the isothermal entropy change of 20 J∙kg−1K−1 and adiabatic temperature change of 3.4 K can be obtained, performing a low-pressure-driven large barocaloric effect. The transition temperature shifts with pressure are as high as −8.8 K∙kbar−1 and −11.8 K∙kbar−1 for forward and reverse transformations, respectively. Such a promising barocaloric performance is mainly attributed to the large entropy change of structural transformation and large volume expansion as high as 3.9%.