Hydrogen and methane are flammable and explosive gases, and their simultaneous measurement holds significant importance in applications of industrial safety and energy transmission. A high-sensitivity multi-parameter sensor based on the surface plasmon resonance (SPR) within an anchor-shaped photonic crystal fiber (AS-PCF) have been proposed and analyzed in detail, which can simultaneously measure hydrogen and methane concentrations while providing temperature self-compensation. To achieve simultaneous detection of hydrogen and methane, an open ring channel is introduced in both the x and y directions of the PCF. Each of these channels is coated with a layer of gold film and gas-sensitive films for hydrogen and methane, respectively. The designed AS-PCF structure is optimized to increase the reactive surface area between the gas and the gas-sensitive films, simultaneously enhancing the energy leakage of core modes to improve sensor performance. In addition, temperature sensitivity is augmented by filling PCF air holes with ethanol and enhancing the asymmetry of the fiber structure. The changes of gas concentration and environmental temperature are derived by demodulating the peak wavelength shifts in the loss and interference spectra. Simulation analysis demonstrates that the sensor can achieve average sensitivities of −0.23 nm/% for hydrogen and −4.84 nm/% for methane within the gas concentration range of 0.5 % to 3 %. Meanwhile, the temperature sensitivity can reach 0.58 nm/°C within the temperature range of 10 °C to 30 °C. This sensor demonstrates excellent linearity and high sensitivity, making it a promising tool for multi-gas measurements in various applications.