For the past decades, recognition technologies of multispectral palmprint have attracted more and more attention due to their abundant spatial and spectral characteristics compared with the single spectral case. Enlightened by this, an innovative robust L2 sparse representation with tensor-based extreme learning machine (RL2SR-TELM) algorithm is put forward by using an adaptive image level fusion strategy to accomplish the multispectral palmprint recognition. Firstly, we construct a robust L2 sparse representation (RL2SR) optimization model to calculate the linear representation coefficients. To suppress the affection caused by noise contamination, we introduce a logistic function into RL2SR model to evaluate the representation residual. Secondly, we propose a novel weighted sparse and collaborative concentration index (WSCCI) to calculate the fusion weight adaptively. Finally, we put forward a TELM approach to carry out the classification task. It can deal with the high dimension data directly and reserve the image spatial information well. Extensive experiments are implemented on the benchmark multispectral palmprint database provided by PolyU. The experiment results validate that our RL2SR-TELM algorithm overmatches a number of state-of-the-art multispectral palmprint recognition algorithms both when the images are noise-free and contaminated by different noises.