Motivated by the Hadamard transforms and center weighted Hadamard transforms, a new class of block center weighted Hadamard transforms (BCWHT) are proposed, which weights the region of mid-spatial frequencies of the signal more than the Hadamard transform. Based on the Kronecker product, directed sum operations, the identity matrix and recursive relations, the proposed one and two dimensions fast block center weighted Hadamard transforms algorithms through sparse matrix factorization are simply obtained.