Coronavirus disease (COVID-19) has infected billion people around the world and affected the economy, but most countries are considering reopening, so the COVID-19 daily confirmed and death cases have increased greatly. It is very necessary to predict the COVID-19 daily confirmed and death cases in order to help every country formulate prevention policies. To enhance the prediction performance, this paper proposes a prediction model based on improved variational mode decomposition by sparrow search algorithm (SVMD), improved kernel extreme learning machine by Aquila optimizer algorithm (AO-KELM) and error correction idea, named SVMD-AO-KELM-error for short-term prediction of COVID-19 cases. Firstly, to solve mode number and penalty factor selection of variational mode decomposition (VMD), an improved VMD based on sparrow search algorithm (SSA), named SVMD, is proposed. SVMD decomposes the COVID-19 case data into some intrinsic mode function (IMF) components and residual is considered. Secondly, to properly selected regularization coefficients and kernel parameters of kernel extreme learning machine (KELM) and improve the prediction performance of KELM, an improved KELM by Aquila optimizer (AO) algorithm, named AO-KELM, is proposed. Each component is predicted by AO-KELM. Then, the prediction error of IMF and residual are predicted by AO-KELM to correct prediction results, which is error correction idea. Finally, prediction results of each component and error prediction results are reconstructed to get final prediction results. Through the simulation experiment of the COVID-19 daily confirmed and death cases in Brazil, Mexico, and Russia and comparison with twelve comparative models, simulation experiment gives that SVMD-AO-KELM-error has best prediction accuracy. It also proves that the proposed model can be used to predict the pandemic COVID-19 cases and offers a novel approach for COVID-19 cases prediction.