With the emergence of the big data age, the issue of how to obtain valuable knowledge from a dataset efficiently and accurately has attracted increasingly attention from both academia and industry. This paper presents a Parallel Random Forest (PRF) algorithm for big data on the Apache Spark platform. The PRF algorithm is optimized based on a hybrid approach combining data-parallel and task-parallel optimization. From the perspective of data-parallel optimization, a vertical data-partitioning method is performed to reduce the data communication cost effectively, and a data-multiplexing method is performed is performed to allow the training dataset to be reused and diminish the volume of data. From the perspective of task-parallel optimization, a dual parallel approach is carried out in the training process of RF, and a task Directed Acyclic Graph (DAG) is created according to the parallel training process of PRF and the dependence of the Resilient Distributed Datasets (RDD) objects. Then, different task schedulers are invoked for the tasks in the DAG. Moreover, to improve the algorithm's accuracy for large, high-dimensional, and noisy data, we perform a dimension-reduction approach in the training process and a weighted voting approach in the prediction process prior to parallelization. Extensive experimental results indicate the superiority and notable advantages of the PRF algorithm over the relevant algorithms implemented by Spark MLlib and other studies in terms of the classification accuracy, performance, and scalability.