The invention relates to a continuous movable type cable climbing device, comprising at least a rack (12) and a climbing device (K) which is composed of an upper roller wheel (1), an upper chain wheel (2), a rotary hinge I (3), a rotary hinge II (4), a rotary hinge III (5), an upper linear driver (6), an upper chain (7), an upper connecting rod (8), a rotary hinge IV (9), a medium chain wheel (10), an electric motor (11), a rotary hinge V (13), a lower connecting rod (14), a lower chain (15), a rotary hinge VI (16), a lower linear driver(17), a rotary hinge VII (18), a rotary hinge VIII (19), a lower chain wheel (20), a lower roller wheel (21); wherein the rack is provided with at least three climbing devices (K).With the cable climbing device of the invention adopted, continuous movement of devices along the cable can be realized; in addition, the cable climbing device features obstacle detouring function.