In this paper, we tackle a backpressure scheduling problem in edge computing networks with a privacy constraint, which requires that two specified packets should not be scheduled to arrive at the same node within a certain time interval. Such a scenario can often be encountered when local models of federated learning are further protected based on secret sharing and secure multi-party computation. We show that such a privacy constraint will lead to a time-varying throughput region. Current throughput-optimal backpressure scheduling strategies may suffer from a severe overall throughput degradation given this constraint. In our algorithm, we enlarge the throughput region in each time slot by introducing a new privacy scale. We further prove that our algorithm can still achieve optimal throughput in each time slot. Simulation results show that compared with existing strategies, our algorithm can effectively reduce the number of privacy collisions in each time slot under the same network configuration and arrival process, which achieves a much larger overall throughput region.