This paper investigates semiparametric estimation of the multivariate elliptical distribution in case dimensionality increases with the sample size. We prove the almost sure convergence and derive the convergence rates of the estimator, depending on the sample size, dimensionality, and the bandwidth of the kernel. As an important by-product, we show almost sure convergence with the corresponding convergence rates for the sample covariance matrix under the Frobenius norm. An extensive simulation study has supported the theory.