Univariate Goncarov polynomials arose from the Goncarov interpolation problem in numerical analysis. They provide a natural basis of polynomials for working with u-parking functions, which are integer sequences whose order statistics are bounded by a given sequence u. In this paper, we study multivariate Goncarov polynomials, which form a basis of solutions for multivariate Goncarov interpolation problem. We present algebraic and analytic properties of multivariate Goncarov polynomials and establish a combinatorial relation with integer sequences. Explicitly, we prove that multivariate Goncarov polynomials enumerate k-tuples of integers sequences whose order statistics are bounded by certain weights along lattice paths in ℕk. It leads to a higher-dimensional generalization of parking functions, for which many enumerative results can be derived from the theory of multivariate Goncarov polynomials.