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We propose a maximum probability model to estimate the origin-destination trip matrix in the networks, where the observed traffic counts of links and the target origin-destination trip demands are independent discrete random variables with known probabilities. The problem is formulated by using the least squares approach in which the objective is to maximize the probability that the sum of squared errors between the estimated values and the observed (target) ones does not exceed a pre-specified threshold. An enumeration so lution approach is proposed to solve the problem in small-sized networks, while a normal approximation based on the central limit theorem is applied in large-sized networks to transform the problem into a deterministic nonlin ear fractional model. Some numerical examples are provided to illustrate the efficiency of the proposed method.