A process for preparing 1-butene from 1-butane, which includes providing a n-butane-containing feed gas stream; introducing of the n-butane-containing feed gas stream into at least one dehydrogenation zone and nonoxidative catalytic dehydrogenation of n-butane; removing hydrogen, the low-boiling secondary constituents and optionally water vapor to give a C.sub.4 product gas stream containing 10-80% by volume of n-butane, 5-40% by volume of 1-butene, 10-50% by volume of 2-butene, 0-40% by volume of butadiene and 0-10% by volume of further gas constituents; introducing the C.sub.4 product gas stream containing 10-80% by volume of n-butane, 10-60% by volume of 1-butene, 15-60% by volume of 2-butene, 0-5% by volume of butadiene and 0-10% by volume of further gas constituents, into a selective hydrogenation zone and selective hydrogenation of butadiene to 1- and/or 2-butene to give stream consisting essentially of n-butane, 1-butene and 2-butene; and separating of the stream distillation into a desired product.