MicroRNAs (miRNAs) are acknowledged as indispensable regulators relevant in many biological processes, and they have been pioneered as therapeutic targets for curing disease. miRNAs are single-stranded, small (19–22 nt) regulatory non-coding RNAs whose deregulation of expression triggers human cancers, including leukemias, mainly through dysregulation of expression of leukemia genes. miRNAs can function as tumour suppressors (suppressing malignant potential) or oncogenes (activating malignant potential) like actors of complex diseases. To address the issue of overcoming instability and low transfection efficiency in vitro, the polyethylene glycol–polyethyleneimine (PEG–PEI) nanoparticle was used as non-viral vector carrier for miR-150 transfection, which is downregulated in chronic myeloid leukemia. PEG–PEI [PEG(550)3-g-PEI(1800)]/miRNA nanocomplexes were synthesised and characterised by particle size distribution (PSD), polydispersity index (PDI) and zeta potential, surface charge, their cytotoxicity, and transfection efficiency. Interaction with human leukemia cells (K-562 and KU812) and control cells NCI-BL2347 with them has been investigated. The transfection efficiency of PEG–PEI/miRNA at N/P 26 rose 6.7-fold above the control by qRT-PCR. The size of homogenous nanocomplexes (PBI < 0.5) was 160.8 ± 11 nm. The data indicate that PEG–PEI may be an encouraging non-viral carrier for altering miRNA expression in the treatment of chronic myeloid leukemia, with many advantages such as relatively high miRNA transfection efficiency and low cytotoxicity.