This study investigates which grid formations and password formats are useful for password authentication by means of eye-gazebased input. Sixteen grid formations were made, in between 3×3 to 6×6 cells (columns-by-rows), for three password formats. The formats were an alphanumeric format, a pattern format, and a picture format. The participants were asked to memorize a 4-object or a 6-object password and register (Task 1), confirm (Task 2), and log in (Task 4) the password on each of the 16 grids with eye-gaze-based input. In Task 3, the participants evaluated each grid with a rating scale. The results showed that task-completion time was mostly shorter for the alphanumeric password format than for the pattern or picture format. Task-completion time of 4-object or 6-object passwords generally increased as the grid density increased, while the task-success rate at the first attempt decreased when the grid density increased. Task-completion time often was longer for grids with more rows than columns (vertical formations, e.g., 3×4 cells) than for grids with more columns than rows (horizontal formations, e.g., 4×3 cells). These results suggest that password authentication with eye-gaze-based input is best performed on horizontal grids with relatively few cells and a traditional (alphanumeric) format.