Quantum communication holds promise for absolutely security in secret message transmission. Quantum secure direct communication is an important mode of the quantum communication in which secret messages are securely communicated over a quantum channel directly. It has become one of the hot research areas in the last decade, and offers both high security and instantaneousness in communication. It is also a basic cryptographic primitive for constructing other quantum communication tasks such as quantum authentication, quantum dialogue and so on. Here we report the first experimental demonstration of quantum secure direct communication with single photons. The experiment is based on the DL04 protocol, equipped with a simple frequency coding. It has the advantage of being robust against channel noise and loss. The experiment demonstrated explicitly the block data transmission technique, which is essential for quantum secure direct communication. In the experiment, a block transmission of 80 single photons was demonstrated over fiber, and it provides effectively 16 different values, which is equivalent to 4 bits of direct transmission in one block. The experiment has firmly demonstrated the feasibility of quantum secure direct communication in the presence of noise and loss.