Hyperspectral images (HSI) contain a great number of bands, which enable better characterization of features. However, the huge dimension and information volume brought by the abundant bands may give rise to a negative influence on the efficiency of subsequent processing on hyperspectral images. Band selection (BS) is a commonly adopted to reduce the dimension of HSIs. Different from the previous work, in this paper, hyperspectral band selection problem is formulated as a multi-objective optimization problem, where the band distribution uniformity among the selected bands and inter-class separation distance from a few labeled samples are optimized simultaneously. To fully exploit the relation between the band subsets with different sizes, we construct a multi-objective evolutionary multi-tasking algorithm for hyperspectral band selection (namely MEMT-HBS) to achieve the selected band subsets for all the selected band sizes in one run. To implement MEMT-HBS, the intra-task pairwise learning based solution generation strategy is suggested to evolve the population for each task to achieve high-quality offspring whose selected band size is restricted to a fixed scope. The inter-task band coverage based knowledge transferring strategy is utilized to choose useful individuals from adjacent tasks to further enhance the performance of current task. Compared with the state-of-the-art semi-supervised and unsupervised BS algorithms, empirical results on different standard hyperspectral datasets show that our proposed MEMT-HBS can determine the superior band subset which has a higher image classification accuracy over the comparison algorithms.