For a set H of graphs, the H-free Edge Deletion problem is to decide whether there exist at most k edges in the input graph, for some k∈ N, whose deletion results in a graph without an induced copy of any of the graphs in H. The problem is known to be fixed-parameter tractable if H is of finite cardinality. In this paper, we present a polynomial kernel for this problem for any fixed finite set H of connected graphs for the case where the input graphs are of bounded degree. We use a single kernelization rule which deletes vertices ‘far away’ from the induced copies of every H∈ H in the input graph. With a slightly modified kernelization rule, we obtain polynomial kernels for H-free Edge Deletion under the following three settings:H contains K1 , s and Kt;H contains K1 , s and the input graphs are Kt-free;H contains Kt and the input graphs are K1 , s-free; where s> 1 and t> 2 are any fixed integers. Our result provides the first polynomial kernels for Claw-free Edge Deletion and Line Edge Deletion for Kt-free input graphs which are known to be NP-complete even for K4-free graphs. © 2016, Springer Science+Business Media New York.