The antileukemia cancer activity of organic compounds analogous to ellipticine representes a critical endpoint in the understanding of this dramatic disease. A molecular modeling simulation on a dataset of 23 compounds, all of which comply with Lipinski’s rules and have a structure analogous to ellipticine, was performed using the quantitative structure activity relationship (QSAR) technique, followed by a detailed docking study on three different proteins significantly involved in this disease (PDB IDs: SYK, PI3K and BTK). As a result, a model with only four descriptors (HOMO, softness, AC1RABAMBID, and TS1KFABMID) was found to be robust enough for prediction of the antileukemia activity of the compounds studied in this work, with an R2 of 0.899 and Q2 of 0.730. A favorable interaction between the compounds and their target proteins was found in all cases; in particular, compounds 9 and 22 showed high activity and binding free energy values of around −10 kcal/mol. Theses compounds were evaluated in detail based on their molecular structure, and some modifications are suggested herein to enhance their biological activity. In particular, compounds 22_1, 22_2, 9_1, and 9_2 are indicated as possible new, potent ellipticine derivatives to be synthesized and biologically tested.