Prokaryotic CRISPR-Cas immune systems are classified into six types based on their effector complexes which cleave dsDNA specifically (types I, II and V), ssRNA exclusively (type VI) or both ssRNA via a ruler mechanism and ssDNA unspecifically (type III). To date, no specific cleavage of ssDNA target has been reported for CRISPR-Cas. Here, we demonstrate dual dsDNA and ssDNA cleavage activities of a subtype I-D system which carries a type III Cas10-like large subunit, Cas10d. In addition to a specific dsDNA cleavage activity dependent on the HD domain of Cas10d, the helicase Cas3' and a compatible protospacer adjacent motif (PAM), the subtype I-D effector complex can cleave ssDNA that is complementary in sequence to the crRNA. Significantly, the ssDNA cleavage sites occur at 6-nt intervals and the cleavage is catalysed by the backbone subunit Csc2 (Cas7), similar to the periodic cleavage of ssRNA by the backbone subunit of type III effectors. The typical type I cleavage of dsDNA combined with the exceptional 6-nt spaced cleavage of ssDNA and the presence of a type III like large subunit provide strong evidence for the subtype I-D system being an evolutionary intermediate between type I and type III CRISPR-Cas systems.