A series of 4H-chromone-1,2,3,4-tetrahydropyrimidine-5-carboxylates derivatives were synthesized via a three component one-pot condensation of chromone-3-carbaldehyde, alkyl acetoacetate, and urea or thiourea, using MCM-41-SO₃H as efficient nanocatalysts and evaluated for their anticancer activity using a combined in silico docking and molecular dynamics protocol to estimate the binding affinity of the title compounds with the Bcr-Abl oncogene. Two programs, AutoDock 4 and AutoDock Vina software were applied to dock the target protein with synthesized compounds and ATP. AutoDock runs resulted in binding energy scores from -7.8 to -10.16 kcal/mol for AutoDock 4 and -6.9 to -8.5 (kcal/mol) for AutoDock Vina. Furthermore, molecular dynamics (MD) simulations are performed using Gromacs for up to 20 ns simulation time investigating the stability of a ligand-protein complex. Finally, a theoretical experiment using MD simulation for 10 ns was performed without defining the initial coordinates, and the affinity binding of ligand to receptors was directly studied, which revealed that the ligand approaches the active sites. The relative free binding energy for the structure 06 (S06), which has the highest binding energy in Autodock 4 and Autodock Vina (-10.10 and -8.5 kcal/mol, respectively), was also evaluated by molecular mechanics (MM) with Poisson-Boltzmann (PB) and a surface area solvation (MM-PBSA) method using g_mmpbsa tools for the last 15 ns MD. On the basis of binding energy scores, a negative binding energy value of 73.6 kcal/mol, S06, was recognized as the dominant potential inhibitors. The cytotoxic properties of S06 was evaluated against three cell lines, acute T cell leukemia (Jurkat), human chronic myelogenous leukemia, (K562) and human foreskin fibroblast (Hu02) using the microculture tetrazolium test MTT assay. Cisplatin was used as the reference agent. The results indicated that S06 has a higher safety index (SI = 0.73, IC50 = 152.64 μg/mL for Jurkat and IC50 = 110.25 μg/mL for Hu02, P < 0.05 means ± SD for four independent experiments) compared to cisplatin (SI = 0.56, IC50 = 8.86 μg/mL for Jurkat and IC50 = 4.96 μg/mL for Hu02). The in silico results indicated that the proposed structures, which have no toxic effects, are potential tyrosine kinase inhibitors (TKIs) that target Bcr-Abl and thus prevent uncontrolled cell growth (proliferation) but not necessarily cell death (apoptosis) and might potentially constitute an interesting novel class of targeted antileukemic drugs, which deserve further studies.