In this study, a nickel–chromium film for detecting strain stress was deposited on 304 stainless steel substrates by the magnetron sputtering technique. The sputtering process parameters were optimized to obtain a better nickel–chromium film. Orthogonal array L16(44) design, signal-to-noise ratio calculation, and variance analysis were performed on the experimental data by the Taguchi method. The influence of the coupling of process parameters such as power, pressure, bias, and substrate temperature on the surface roughness, deposition rate, and resistivity of the film was studied. The power is the most significant influence factor affecting the film’s performance indicators, and the contribution rates of each process parameter to the response variables and the regression equation of each response variable are obtained. Finally, the gray correlation analysis results of the response variables show that at conditions of 200 W power, 1.6 Pa pressure, −100 V bias, and 400 °C substrate temperature, the surface roughness of the nickel–chromium film is 55 nm, the deposition rate is 110 nm/min, and the resistivity is 1.10 × 10−4 Ω cm. It can be seen that the best film performance parameter group can be obtained using the Taguchi gray correlation method under the multi-parameter coupling of the nickel–chromium thin-film.