A hydraulic control device of an automatic transmission configured such that: a first gear stage is formed by engagement of an LR brake and a low clutch; a third gear stage by engagement of the low clutch and an R35 brake; and a reverse gear stage by engagement of the LR brake and the R35 brake. The hydraulic control device includes a cut valve configured to be switched between a first state where a source pressure port of a third linear solenoid valve (SV) configured to control an oil pressure supplied to the R35 brake is connected to an oil pressure source and a second state where the pressure is discharged from the port. The cut valve becomes the second state when the third gear stage is shifted to the first gear stage, and the oil pressure supplied to the low clutch is less than a predetermined oil pressure.