The aim of this paper is to construct a canonical nonlinear connection $\Gamma =(M_{\left(\alpha \right)\beta }^{\left(i\right)},N_{\left(\alpha \right)j}^{\left(i\right)})$ on the 1-jet space $J^1(T,M)$ from the Euler-Lagrange equations of the quadratic multi-time Lagrangian function $$L=h^{\alpha \beta }\left(t\right)g_{ij}(t,x)x_{\alpha }^i{x}_{\beta }^j+U_{\left(i\right)}^{\left(\alpha \right)}(t,x)x_{\alpha }^i+F(t,x).$$