We propose a scheme for the generation of narrowband triphoton frequency-entangled states. This scheme uses the four-wave mixing and the electromagnetically induced transparency in two cold-atom ensembles. By using the second-order perturbation theory, some relevant calculations are performed. By analyzing the coincidence-counting rate, we study the correlation and nonclassical properties of these states, and find that they have a similar feature to that of the discrete-variable W state, and can show the antibunching effect.