Recently single neurons measurements during perceptual decision tasks in monkeys have coupled the neural mechanisms of decision making and the establishment of a degree of confidence. These neural mechanisms have been investigated in the context of a spiking attractor network model. It has been shown that confidence about a decision under uncertainty can be computed using a simple neural signal in individual trials. However, it remains unclear if a neural attractor network can reproduce the behavioral effects of confidence in humans. To answer this question, we designed an experiment in which participants were asked to perform an orientation discrimination task, followed by a confidence judgment. Here we show for the first time that an attractor neural network model, calibrated separately on each participant, accounts for full sequences of decision-making. Remarkably, the model is able to reproduce quantitatively the relations between accuracy, response times and confidence, as well as various sequential effects such as the influence of confidence on the subsequent trial. Our results suggest that a metacognitive process such as confidence in perceptual decision can be based on the intrinsic dynamics of a nonlinear attractor neural network.