To overcome rubber tree (RT) tissue culture explant source limitations, the current study aimed to establish a new Hevea brasiliensis somatic embryogenesis (SE) system, laying the technical foundation for the establishment of an axillary-bud-based seedling regeneration system. In this study, in vitro plantlets of Hevea brasiliensis Chinese Academy of Tropical Agricultural Sciences 917 (CATAS 917) were used as the experimental materials. Firstly, the optimum conditions for axillary bud swelling were studied; then, the effects of phenology, the swelling time of axillary buds (ABs), and medium of embryogenic callus induction were studied. Plantlets were obtained through somatic embryogenesis. Flow cytometry, inter-simple sequence repeat (ISSR molecular marker) and chromosome karyotype analysis were used to study the genetic stability of regenerated plants along with budding seedlings (BSs) and secondary somatic embryo seedlings (SSESs) as the control. The results show that the rubber tree’s phenology period was mature, and the axillary bud induction rate was the highest in the 2 mg/L 6-benzyladenine (6-BA) medium (up to 85.83%). Later, 3-day-old swelling axillary buds were used as explants for callogenesis and somatic embryogenesis. The callus induction rate was optimum in MH (Medium in Hevea) + 1.5 mg/L 2,4-dichlorophenoxyacetic acid (2,4-D) + 1.5 mg/L 1-naphthalene acetic acid (NAA) + 1.5 mg/L Kinetin (KT) + 70 g/L sucrose (56.55%). The regenerated plants were obtained after the 175-day culture of explants through callus induction, embryogenic callus induction, somatic embryo development, and plant regeneration. Compared with the secondary somatic embryo seedling control, axillary bud regeneration plants (ABRPs) were normal diploid plants at the cellular and molecular level, with a variation rate of 7.74%.