Catalyzes the synthesis of cardiolipin (CL) (diphosphatidylglycerol) by specifically transferring a phosphatidyl group from CDP-diacylglycerol to phosphatidylglycerol (PG). Cannot catalyze the phosphatidyl group transfer from one PG molecule to another to form CL. Possesses high activity with PG species carrying dioleoyl groups and low activity with species carrying one or two palmitoyl groups. CL is a key phospholipid in mitochondrial membranes and plays important roles in maintaining the functional integrity and dynamics of mitochondria under both optimal and stress conditions. In mitochondrial fission, CL stabilizes the protein complex of the major mitochondrial fission factors, DRP3A and DRP3B. 1,2-diacyl-sn-glycero-3-phospho-(1'-sn-glycerol) + a CDP-1,2-diacyl-sn-glycerol = a cardiolipin + CMP + H(+) Optimum pH is about 9.0. Strong dwarf phenotype, small siliques with only a few small-sized and sterile seeds, when grown in long day conditions under low light. Dysfunction of mitochondria: abnormal ultrastructure, reduced content of respiratory complex I/complex III supercomplexes and marked accumulation of tricarboxylic acid cycle derivatives and amino acids. Belongs to the CDP-alcohol phosphatidyltransferase class-I family.