Qudit quantum system can carry more information than that of qubit, so it is an important resource in quantum information processing. The ququart state with the tensor representation is gotten in term of the photon entangled state. The necessary and sufficient condition for realizing a successful or perfect teleportation is obtained, as will be shown, this condition is determined by the measurement matrix and the quantum channel parameter matrix. The general expressions of the measurement matrix are written out and the quantum channel parameter matrix are discussed. Furthermore, the teleportation of ququart state is proposed via different kinds of quantum channels. The description of the teleporting process with the help of tensor analysis is more compact and clear.