As an important microstructure, columnar crystal growth technology, especially the growth technology of single columnar crystal plays an important role in improving the performances of semiconductor, optical devices and other related products. In many practical applications, because the alloy is composed of multi-component and there is inevitably flow in the melt, it is necessary to study the growth of columnar crystals in multi-component melt with flow separately. The growth of columnar crystal in a ternary undercooled melt subjected to straining flow under non-isothermal conditions is studied, and the approximate analytical expression for growth morphology of columnar crystal is given by using asymptotic method. It can be seen from the expression that straining flow is an important reason for irregular columnar crystal. When analyzing the effect of straining flow on the growth of columnar crystal in ternary melt, it is found that the incoming flow accelerates the growth velocity of the interface, while the outgoing straining flow reduces the growth velocity of the interface, namely, the straining flow makes the interface of columnar crystal deformed. At the same time, it is found that the interface deformation becomes more intense with the increase of flow velocity. The above conclusion can also be applied to the effect of straining flow on the interface morphology of columnar crystal in pure melt and binary melt. The comparison of the effects of straining flow on the interface of columnar crystal among pure melt, binary melt and ternary melt, shows that the interface morphology of columnar crystal in dilute alloy melt is more affected by straining flow than in the pure melt, but the more components are more easily affected by flow. However, the number of components in melt is not a decisive factor for the change of interface morphology of the columnar crystal, but the constitutional undercooling is an important factor for determining the interface morphology of multicomponent alloy. According to the conclusion of this paper, the influence of straining flow on the interface morphology of columnar crystal growth can be quantitatively predicted, which provides the necessary theoretical guidance in accurately controlling the interface morphology in the future.