We propose a design of ultra-compact plasmonic coherent perfect absorber (CPA) working in the near-infrared band. The main operating mechanism is the magnetic-dipole resonant coherent absorption in the metal-insulator-metal waveguide, which enables the CPA in the near-infrared band and can be also flexibly adjusted to place the magnetic-dipole resonance at any position in the near-infrared band. Numerical analysis verifies our proposal that the magnetic resonant CPA is crucial for near-IR CPA in the ultra-compact metal-insulator-metal waveguide.