Abstract Dempster–Shafer (D–S) evidence theory is useful in the realm of multi-source data fusion. However, a counterintuitive result may be obtained when the belief probability assignments (BPAs) are highly conflicting. To overcome this flaw, in this paper a symmetric fractal-based belief Kullback–Leibler divergence (F B D S K L) is proposed. It is used to measure the divergence between BPAs, and is more capable than the existing belief divergence methods in measuring the conflict between two BPAs in numerical examples. Furthermore, the proposed F B D S K L is proved to have desirable properties including nonnegativity, nondegeneracy and symmetry. To apply F B D S K L divergence measure to practical problems, a novel F B D S K L-based multi-source data fusion (F B D S K L-MSDF) algorithm is designed. Through comparisons with the well-known related methods, the proposed F B D S K L-MSDF algorithm is validated to be superior and more robust. Finally, the proposed F B D S K L-MSDF is applied to two real-world classification problems to verify its high practicability.