For achieving high efficiency fiber Bragg gratings (FBGs) utilizing infrared femtosecond laser point-by-point inscription method, it is crucial to make the inscribed periodic structure perfectly in phase. It requires a perfect alignment between the micrometer-sized laser spot with the fiber along the length. Here we report the highly precise fabrication of FBGs by infrared femtosecond laser point-by-point direct-writing method. Image recognition technique is applied to for automatically aligning the trace of the laser spot with the referenced central axis of the fiber along the whole FBG length. FBGs inscription with high spatial precision is confirmed by multiple approaches, including microscopic photographing and FBG spectroscopic measurement. 50 mm-long uniform FBGs with high reflectivity have been successfully demonstrated in a small-core single-mode silica fiber using auto-aligning technique.