We propose a class of almost rate-1 construction for 2n-bit hash functions, based on (2n, n) blockciphers, where 2n is the length of the cipher key and n is the cipher block length. These hash functions we proposed are proved to be optimum collision resistance and preimage resistance in the ideal cipher model. The hash rate of the construction is l−1/l where l is the number of cipher calls in the compression function. The hash rate is closed to 1 if l is large. Compare with existing DBL hash functions based on block ciphers with optimum collision resistance and preimage resistance, they are more efficient and simpler.