This paper considers parameter estimation for state-space models (SSMs). We propose quasi-likelihood (QL) and asymptotic quasilikelihood (AQL) approaches for the estimation of state-space models. The asymptotic quasi-likelihood (AQL) utilises a nonparametric kernel estimator of the conditional variance covariances matrix Σt to replace the true Σt in the standard quasi-likelihood. The kernel estimation avoids the risk of potential miss-specification of Σt and thus make the parameter estimator more robust. This has been further verified by empirical studies carried out in this paper.