This paper studies the modeling and synchronization problems for stochastic complex dynamical networks subject to consecutive packet dropouts. Different from some existing research results, both probability characteristic and upper bound of consecutive packet dropouts are involved in the proposed approach of controller design. First, an error dynamical network with stochastic and bounded delay is established by step-delay method, where the randomness of the bounded delay can be verified later by the probability theory method. A new modeling method is introduced to reflect the probability characteristic of consecutive packet dropouts. Based on the proposed model, some sufficient conditions are proposed under which the error dynamical network is globally exponentially synchronized in the mean square sense. Subsequently, a probability-distribution-dependent controller design procedure is then proposed. Finally, two numerical examples with simulations are provided to validate the analytical results and demonstrate the less conservatism of the proposed model method.