DNA has become a promising material to construct high-order structures and molecular devices owing to its sequence programmability. Herein, a DNA machine based on branched catalytic hairpin assembly (bCHA) is introduced for dynamic self-assembly of DNA dendrimers. For this system, a Y-shaped hairpin trimer tethered with three kinds of hairpins (H1, H2 and H3) is constructed. The introduction of an initiator (I) triggers a cascade of CHA reactions among hairpin trimers, leading to the formation of DNA dendrimers. Through labeling fluorophore/quencher pairs in the hairpin trimers, this catalytic DNA machine is applied as a versatile amplification platform to analyze nucleic acids using microRNA-155 (miR-155) as a model analyte. Benefiting from the "diffusion effect", the proposed bCHA achieves a greatly improved sensitivity in comparison with traditional CHA. This catalytic amplifier exhibits high sensitivity toward miR-155 detection with a dynamic range from 2.5 nM to 500 nM and demonstrates excellent selectivity to distinguish the single-base mismatched sequence from the perfectly complementary one, which is further applied to detect low-abundance miR-155 spiked in complex matrices with minimal interference. This method is further applied for imaging of miR-155 in different live cells. The bCHA reaction can be specifically triggered by intracellular miR-155, achieving monitoring of the dynamic miRNA expression and distribution. Overall, our proposed enzyme-free dynamic DNA self-assembly strategy provides a versatile approach for the development of DNA nanotechnology in biosensing and bioimaging, and monitoring the cellular miRNA-related biological events.