When a vehicle is halted with the transmission in a forward drive range, an input clutch is disengaged to enhance the fuel efficiency and, at the same times a hill-hold brake is engaged to prevent the vehicle from rolling backward on a steep up-slope. At that time, the hydraulic pressure P.sub.C-1 of the input clutch C1 is gradually reduced by .DELTA.P.sub.CIR (P.sub.C-1 =P.sub.C-1 -.DELTA.P.sub.CIR) while the hydraulic pressure P.sub.B-1 of the hill-hold brake B1 is increased gradually so as to satisfy an equation P.sub.B-1 =K1+K2 X e where .DELTA.P.sub.cir is a change in hydraulic pressure which is required for gradually disengaging the first clutch C1, K1 is a hill-hold brake pressure at which braking resistance begins, K2 is hill-hold brake pressure producing a fully braked condition, and e is the input/output rotational-speed ratio of a torque converter Subsequently during start of vehicle movement, the hydraulic pressure P.sub.C-1 of the input clutch C1 is gradually increased (P.sub.C-1 =p.sub.C-1 +.DELTA.P.sub.C-1A) while the hydraulic pressure P.sub.B-1 of the hill-hold brake B1 is gradually decreased (P.sub.B-1 ==P.sub.B-1-.DELTA.P.sub.B-1) until the ratio of the rotational speed N.sub.C-1 of the first clutch C1 becomes less than a rotational speed N.sub.C-1E corresponding to the clutch being almost engaged .DELTA.P.sub.C-1A and .DELTA.P.sub.B-1 are incremental values proportional to accelerator depression so that a delay in starting is reduced in accordance with driver demand.