The ability to intercept uncooperative targets is key to many diverse flight behaviors, from courtship to predation. Previous research has looked for simple geometric rules describing the attack trajectories of animals, but the underlying feedback laws have remained obscure. Here we use GPS loggers and onboard video cameras to study peregrine falcons Falco peregrinus attacking stationary targets, maneuvering targets, and live prey. We show that the terminal attack trajectories of peregrines are not described by any simple geometric rule as previously claimed, and instead use system identification techniques to fit a phenomenological model of the dynamical system generating the observed trajectories. We find that these trajectories are best – and exceedingly well – modelled by the proportional navigation (PN) guidance law used by most guided missiles. Under this guidance law, turning is commanded at a rate proportional to the angular rate of the line-of-sight between the attacker and its target, with a constant of proportionality (i.e. feedback gain) called the navigation constant (𝑁). Whereas most guided missiles use navigation constants falling on the interval 3 ≤ 𝑁 ≤ 5, peregrine attack trajectories are best-fitted by lower navigation constants (median 𝑁 < 3). This lower feedback gain is appropriate to the lower flight speed of a biological system, given its presumably higher error and longer delay. This same guidance law could find use in small visually-guided drones designed to remove other drones from protected airspace.