A new synthetic strategy for the construction of two polypropionate subunits of discodermolide, a highly potent anticancer natural product, is reported. The strategy relies on two key reactions: a Shimizu non‐aldol reaction, a stereoselective hydrogenolysis of alkenyl epoxides, to generate the syn hydroxy‐methyl moiety and a NaBH4‐BF3.OEt2 mediated hydride addition reaction. By utilizing this strategy, two different fragments of discodermolide, C9‐C13 subunit and C15‐C21 subunit have been successfully synthesized.