Recent studies have described leukaemia stem cells (LSCs) as being central to the initiation, growth, and relapse of acute myelogenous leukaemia (AML). However, to date, very few small molecules have been shown to directly target this LSC population. The present study, for the first time, demonstrates that peperomin E (PepE), a naturally occurring secolignan, induces apoptosis in cultured AML and LSC-like cell lines, while sparing normal bone marrow stromal cells (hBMSCs). Furthermore, a series of eighteen amino derivatives was synthesised through a diastereoselective conjugate addition of several primary and secondary amines to the α-methylene-γ-butyrolactone moiety of PepE to increase its water-solubility and anti-AML/LSC activity. The synthesised amino analogues were evaluated for in vitro cytotoxicity against AML cell lines (KG-1, HL-60, THP-1) and an LSC-like cell line (KG-1a CD34⁺CD38⁻). Most of the secondary open-chain amine derivatives showed enhanced water solubility and high activities against AML/LSC cells. The most potent compound, 6, derived from N-methylethanolamine, exhibited exclusive cytotoxicity against KG-1a CD34⁺CD38⁻ cells, with an IC₅₀ value of 0.5 ± 0.1 μM, which was 13-fold more potent than PepE. Moreover, compound 6 showed low toxicity against hBMSCs (inhibition of 11.2% at 50 μM). Preliminary mechanistic studies revealed that compound 6 could induce apoptosis of KG-1a CD34⁺CD38⁻ cells. Therefore, we propose that compound 6 should be tested further for its in vivo activity and safety with the aim to develop it as a new type of drug for LSC-targeted therapy.