We propose a pulsed neural network model for visual search tasks. The traditional saliency-based search model can well simulate a simple visual search task, however, it can not account for other interesting phenomenon, for example, search asymmetry. Previous models with a deterministic WTA always direct attention to the most salient location, regardless of relative saliency. Thus, variation of the saliency does not lead to variation of search efficiency in the saliency-based search models. We show that the introduction of a stochastic WTA enables the saliency-based search model to exhibit changes in search efficiency as a result of the variation of the relative saliency, taking into account due to stochastic shifts of attention. The proposed model can simulate not only simple visual search tasks but also various asymmetries in visual searches.