Remaining useful life (RUL) prediction of lithium-ion battery in early-cycle stage is of great significance to improve battery performance and reduce losses caused by failure. Due to complex degradation mechanism and insufficient data in early-cycle stage, current RUL prediction schemes for lithium-ion battery have trouble obtaining degradation characteristics to achieve satisfactory prediction accuracy. Aiming at this problem, this paper proposes an RUL prediction method of lithium-ion batteries in early-cycle stage based on similar sample fusion under Lebesgue sampling framework. First, a novel similarity measurement index based on fusion of Pearson correlation coefficient and Euclidean distance is proposed, and the fusion parameter is optimized by jumping spider optimization algorithm. Similar samples are selected as reference for the prediction model. Then, Lebesgue sampling theory is introduced to complete data structure transformation for similar samples, so as to ensure that the fused points of different similar samples are under the same degradation state. Finally, similar sample fusion result is transformed to Riemann sampling framework and perform a linear fitting. Fitting results are used to construct a particle filter model for capacity degradation process and RUL prediction. Experimental results and comparison studies on APR18650M1A battery dataset demonstrate the effectiveness of the proposed method.