For　a　class　of　nonlinear　systems　with　uncertain　parameters,　this　paper　proposes　a　novel　data-driven　adaptive　control　method.　This　method　utilizes　a　designed　parameter　estimator　to　steer　the　closed-loop　system　to　the　predefined　ideal　system　on　the　manifold.　It　achieves　finite-time　convergence　of　the　system　through　a　terminal　sliding　mode　controller.　Based　on　the　data-driven　concept,　the　parameter　regression　matrix　is　expanded　to　acquire　the　unknown　parameters　of　the　system　indirectly.　By　introducing　a　perturbation　matrix,　the　issue　that　the　expanded　parameter　regression　matrix　needs　to　satisfy　certain　excitation　conditions　to　be　full-rank　is　overcome,　and　an　algebraic　equation-based　parameter　estimator　is　constructed　to　achieve　an　arbitrary　small　convergence　of　the　parameter　estimation　error.　A　global　non-singular　fast　terminal　sliding　mode　controller　is　designed　for　the　system　on　the　manifold,　achieving　finite-time　convergence　of　the　system.　The　stability　of　the　closed-loop　system　is　verified　through　Lyapunov-based　stability　analysis.　As　an　application,　the　effectiveness　and　superiority　of　the　proposed　method　are　validated　through　numerical　simulations　of　Euler-Lagrange　systems　with　unknown　inertia　parameters.