GPUs have become thedefactohardware devices for accelerating Deep Neural Network (DNN) inference workloads. However, the conventionalsequential execution mode of DNN operatorsin mainstream deep learning frameworks cannot fully utilize GPU resources, even with the operator fusion enabled, due to the increasing complexity of model structures and a greater diversity of operators. Moreover, theinadequate operator launch orderin parallelized execution scenarios can lead to GPU resource wastage and unexpected performance interference among operators. In this paper, we proposeOpara, a resource- and interference-aware DNNOperatorparallel scheduling framework to accelerate DNN inference on GPUs. Specifically,Oparafirst employsCUDA StreamsandCUDA Graphtoparallelizethe execution of multiple operators automatically. To further expedite DNN inference,Oparaleverages the resource demands of operators to judiciously adjust the operator launch order on GPUs, overlapping the execution of compute-intensive and memory-intensive operators. We implement and open source a prototype ofOparabased on PyTorch in anon-intrusivemanner. Extensive prototype experiments with representative DNN and Transformer-based models demonstrate thatOparaoutperforms the default sequentialCUDA Graphin PyTorch and the state-of-the-art operator parallelism systems by up to$1.68\boldsymbol{\times}$and$1.29\boldsymbol{\times}$, respectively, yet with acceptable runtime overhead.