Grafting polar polysiloxanes to addition-cure liquid silicone rubber (ALSR) is a promising method to improve its adhesion performance. Herein, we synthesized a novel silicone adhesion promoter containing phenolic hydroxyl and acrylate groups via hydrosilylation reaction, denoted as PMHS-g-(EE/TD). It was found that PMHS-g-(EE/TD) effectively enhanced the bond strength of ALSR with polycarbonate (PC) and polyamide (PA) substrates. When the PMHS-g-(EE/TD) content was 2 phr, the bond strength of ALSR with PC and PA substrates were 3.8 MPa and 3.1 MPa, respectively. More importantly, after being heat-treated at 150 °C for 72 h or soaked in 25 °C distilled water for 8 h, the bond strength of ALSR/PMHS-g-(EE/TD) with PC and PA substrates maintained a rather high value. The adhesion promotion mechanism of PMHS-g-(EE/TD) for ALSR was further discussed and revealed. On the one hand, PMHS-g-(EE/TD) participated in the curing process of ALSR through CC bonds and formed chemical bond connections with the ALSR chain; on the other hand, PMHS-g-(EE/TD) was enriched on the ALSR surface to establish a boundary layer containing –OH and –COO, forming hydrogen bonds with the substrate. PMHS-g-(EE/TD) acted as a bridge to tightly connect the substrate and ALSR, which greatly improved the adhesion performance. This work provides a simple approach to fabricating ALSR with prominent adhesive properties.