Increasing ship traffic and human activity in the Arctic has led to a growing demand for accurate Arctic weather forecast. High-quality forecasts obtained by models are dependent on accurate initial states achieved by assimilation of observations. In this study, a multi-variate nudging (MVN) method for assimilation of sea-ice variables is introduced. The MVN assimilation method includes procedures for multivariate update of sea-ice volume and concentration, and for extrapolation of observational information spatially. The MVN assimilation scheme is compared with the Ensemble Kalman Filter (EnKF) using the Los Alamos Sea Ice Model. Two multi-variate experiments are conducted: in the first experiment, sea-ice thickness from the European Space Agency's Soil Moisture and Ocean Salinity mission is assimilated, and in the second experiment, sea-ice concentration from the ocean and Sea Ice Satellite Application Facility is assimilated. The multivariate effects are cross-validated by comparing the model with non-assimilated observations. It is found that the simple and computationally cheap MVN method shows comparable skills to the more complicated and expensive EnKF method for multivariate update. In addition, we show that when few observations are available, the MVN method is a significant model improvement compared to the version based on one-dimensional sea-ice concentration assimilation.