Climbing plants with tendrils show search and coiling behaviour. A tendril searches for a host object and then twines around it. Subsequently, the tendril coils to pull the main stem of the climbing plant close to the host object. Furthermore, the stems may also twine around the host object. In this paper, we propose a procedural approach to incrementally constructing virtual climbing plants with tendrils that mimic such behaviour. We developed several simple rules to guide the construction process. Although our approach is not based on a physical or biological concept, it is fast and efficient in generating climbing plants with tendrils, with acceptable quality. We propose techniques that are useful for enhancing the realism of climbing plants in close-up view.