Motivated by the crucial role played by the discrete flavour symmetry groups in explaining the observed neutrino oscillation data, we consider the application $A_4$ modular symmetry in the linear seesaw framework. The basic idea behind using the modular symmetry is to minimize the usage of multiple flavon fields having specific vacuum expectation value (VEV) alignments. The breaking of flavor symmetry takes place when the complex modulus $\tau$ acquires VEV. Linear seesaw in this framework is realized with six heavy $SU(2)_L$ singlet fermion superfields and a weighton. We discuss the phenomena of neutrino mixing and show that the obtained mixing angles and CP violating phase in this framework are compatible with the observed $3\sigma$ range of the current oscillation data. In addition, we also investigate the phenomenon of leptogenesis arising from the decay of lightest heavy fermion superfield to explain the observed baryon asymmetry of the Universe.