Private Information Retrieval (PIR) allows a user to retrieve the $(i)$th bit of an $(n)$-bit database without revealing to the database server the value of $(i)$. In this paper, we present a PIR protocol with the communication complexity of $(O(gamma log n))$ bits, where $(gamma)$ is the ciphertext size. Furthermore, we extend the PIR protocol to a private block retrieval (PBR) protocol, a natural and more practical extension of PIR in which the user retrieves a block of bits, instead of retrieving single bit. Our protocols are built on the state-of-the-art fully homomorphic encryption (FHE) techniques and provide privacy for the user if the underlying FHE scheme is semantically secure. The total communication complexity of our PBR is $(O(gamma log m+gamma n/m))$ bits, where $(m)$ is the number of blocks. The total computation complexity of our PBR is $(O(mlog m))$ modular multiplications plus $(O(n/2))$ modular additions. In terms of total protocol execution time, our PBR protocol is more efficient than existing PBR protocols which usually require to compute $(O(n/2))$ modular multiplications when the size of a block in the database is large and a high-speed network is available.