In this study, we consider $\psi$-Caputo fractional Langevin dynamical system with impulses. We establish necessary and sufficient conditions to ensure the total controllability of the linear Langevin impulsive system. Additionally, we establish some criteria to ensure the controllability of the considered nonlinear system. We transform the problem of controllability into a task of finding a fixed point. We use fractional calculus, Mittag-Leffler functions, Gramian-type matrices, and Schauder`s fixed point technique to derive our main results. Finally, we provide a numerical example to check the validity and accuracy of our results.