Surface plasmon resonance (SPR) sensors are among the most sensitive sensors. In such devices, a grating is a compelling alternative to a prism for the excitation of a surface plasmon, especially in the development of sensors for point-of-care applications due to their compactness and cost-effectiveness. Here, we demonstrate the use of a tunable laser in a grating-based SPR system for further miniaturization and integration. The tunable laser working at normal incidence replaces spectral and moving components, while also simplifying the optical setup. Normal incidence is conventionally avoided due to the complexity of the control of degenerated SPR modes. We investigate, both computationally and experimentally, the splitting of the SPR modes at small nonzero incidences, which is lacking in previously reported studies. By optimizing the grating configuration, we were able to diminish the SPR mode splitting phenomenon when the excitation was feasible with the normal incidence configuration. The fabricated sensor showed a high sensitivity of 1101.6 nm/RIU. Notably, the figure of merit of the sensor, defined as the ratio between the sensitivity and bandwidth of the SPR dip, was 229.5. The experimental results were consistent with the simulation results. We also demonstrate its capability for detecting low concentrations of glucose and creatinine with the limit of detection of 14.2 and 19.1 mmol/L, respectively.