This paper studies estimation of multivariate parametric jump-diffusions based on Wagner-Platen strong approximations. The first two conditional moments are derived based on an approximate numerical solution to the jump-diffusion and they are used to construct the quasi-likelihood function. The estimation method is applicable to a general class of multivariate jump-diffusions, capable of estimating both jump intensity and parameters in jump amplitude. Monte Carlo simulation shows that the proposed method has good finite sample property, and an application to the Merton jump-diffusion model with Dow Jones 30 stock data is also discussed.