A chemical wave train propagating in a narrowing excitable channel surrounded by a nonexcitable field is investigated by using a photosensitive Belousov-Zhabotinsky (BZ) reaction. The considered geometry is created as a dark triangle surrounded by an illuminated area where the reaction is suppressed by the light-induced generation of bromide ion. For a low illumination level, a pulse train terminates at a constant position. However, as the light intensity increases, the position at which subsequent pulses disappear changes periodically, so that the period-doubling of penetration depth occurs. Two-dimensional simulations based on a modified Oregonator model for the photosensitive BZ reaction reproduce the essential features of the experimental observation.