An experimental apparatus was designed to study the non-shock initiation reaction evolution process of a HMX (cyclotetramethylenete-tranitramine)-based pressed PBX (Plastic Bonded Explosive)-A column under the main constraint of the inertial mass of the explosive bulk, with strong bottom and circumferential confinements and with the strength of a PMMA plate cover as the threshold to control the internal reaction pressure. The HMX-based pressed PBX-A column was ignited by black powder. The experimental results show that the reaction violence was quite mild, and the estimated amount of explosive consumed at the time of the PMMA plate cracking was only 1.8% of the thickness. The velocity curve of the constrained surface shows that the internal reaction pressure at the initial stage of the structural deformation shows the “quasi-isobaric” characteristic, and the estimated reaction pressure at this stage was about 157.41 MPa.