Curved texturing is an effective technique to improve the skid-resistance performance of concrete pavements, which relies on the suitable combination of the groove parameters. This study aims to optimize these parameters with the consideration of skid-resistance performance and driving stability. A pressure film was adopted to obtain the contact stress distribution at the tire–pavement interface. The evaluated indicator of the stress concentration coefficient was established, and the calculation method for the stationary steering resistance torque was optimized based on actual tire–pavement contact characteristics. Test samples with various groove parameters were prepared use self-design molds to evaluate the influence degree of each groove parameter at different levels on the skid-resistance performance through orthogonal and abrasion resistance tests. The results showed that the groove depth and groove spacing had the most significant influence on the stress concentration coefficient and stationary steering resistance torque, respectively, with the groove depth having the most significant influence on the texture depth. Moreover, the driving stability and durability of the skid-resistance performance could be balanced by optimizing the width of the groove group. After analyzing and comprehensively comparing the influences of various parameters, it was found the parameter combination with width, depth, spacing, and the groove group width, respectively, in 8 mm, 3 mm, 15 mm, and 50 mm can balance the skid-resistance performance and driving stability. The actual engineering results showed that the R2 of the fitting between the stress concentration coefficient and SFC (measured at 60 km/h) was 0.871, which proved the effectiveness of the evaluation index proposed in this paper.