This paper focuses on the development of a prognostic scheme for estimating the remaining useful life (RUL) of Lithium-ion batteries with missing observations. The scheme has two main modules based on extreme learning machines: pre-processing and prediction. The pre-processing module uses novel single and multiple imputation techniques to estimate the missing observations. The prediction module aims to obtain precise predictions even in the presence of missing observations and with the related uncertainty. The pre-processing module sends imputed subsets of samples to the prediction module, which makes use of extreme learning machines for one-step and multi-steps predictions. The prediction module contains various multi-steps prediction strategies including iterative, direct and DirRec, which use the constant-current experimental capacity data for the long-term prediction of the remaining useful life. Accurate prediction of RUL requires continuity in the time-series dataset. The proposed scheme is designed to build an intelligent prediction system with the ability to handle time-series data containing missing values and is robust enough to generate a complete time-series dataset and, then, make short or long term predictions. The experimental results confirm that the proposed framework can be beneficial for intelligent diagnostic and prognostic systems related to battery as well as other wide range of applications. The main focus of the paper is the development of an integrated imputation-prediction scheme and not the evaluation of individual performances of the imputation or prediction techniques.