Photonic time-delay reservoir computing (TDRC) using a self-injection locked semiconductor laser under optical feedback from a narrowband apodized fiber Bragg grating (AFBG) is proposed and numerically demonstrated. The narrowband AFBG suppresses the laser's relaxation oscillation and provides self-injection locking in both the weak and strong feedback regimes. By contrast, conventional optical feedback provides locking only in the weak feedback regime. The TDRC based on self-injection locking is first evaluated by the computational ability and memory capacity, then benchmarked by the time series prediction and channel equalization. Good computing performances can be achieved using both the weak and strong feedback regimes. Interestingly, the strong feedback regime broadens the usable feedback strength range and improves robustness to feedback phase variations in the benchmark tests.