An apparatus and method for computing a SHA-1 hash function value are provided. The apparatus includes a first register unit including a plurality of registers that store a first bit string of predetermined lengths for generation of a hash function value; a second register unit storing input data in units of second bit strings with predetermined lengths, and sequentially outputting the second bit strings; a third register unit performing an operation on the first bit string of the plurality of registers and the second bit strings output from the second register unit so as to generate and store a third bit string, and updating first-bit string of the plurality of registers based on the third bit string; and an adding unit combining the first bit string stored in the first register unit, the first bit string of the third bit string stored in the third register unit, and the original initial values stored in the first register unit so as to obtain a hash function value. Accordingly, it is possible to reduce the size of the apparatus and stably compute a hash function value at a high speed.