  In the framework of the topcolor-assisted technicolor (TC2) models, we study
the production of the top-pions $\pi^{0}_{t}$, $\pi_{t}^{\pm}$ via the
processes $ep\to\gamma c\to\pi^{0}_{t}c$ and $ep\to\gamma c\to\pi^{\pm}_{t}b$
mediated by the anomalous top coupling $tc\gamma$. We find that the production
cross section of the process $ep\to\gamma c\to\pi^{0}_{t}c$ is very small. With
reasonable values of the parameters in TC2 models, the production cross section
of the process $ep\to\gamma c\to\pi^{\pm}_{t}b$ can reach $ 1.2pb$. The charged
top-pions $\pi^{\pm}_{t}$ might be directly observed via this process at the
THERA collider based $\gamma p$ collisions.
