In the era of big data, practical applications in various domains continually generate large-scale time-series data. Among them, some data show significant or potential periodicity characteristics, such as meteorological and financial data. It is critical to efficiently identify the potential periodic patterns from massive time-series data and provide accurate predictions. In this paper, a Periodicity-based Parallel Time Series Prediction (PPTSP) algorithm for large-scale time-series data is proposed and implemented in the Apache Spark cloud computing environment. To effectively handle the massive historical datasets, a Time Series Data Compression and Abstraction (TSDCA) algorithm is presented, which can reduce the data scale as well as accurately extracting the characteristics. Based on this, we propose a Multi-layer Time Series Periodic Pattern Recognition (MTSPPR) algorithm using the Fourier Spectrum Analysis (FSA) method. In addition, a Periodicity-based Time Series Prediction (PTSP) algorithm is proposed. Data in the subsequent period are predicted based on all previous period models, in which a time attenuation factor is introduced to control the impact of different periods on the prediction results. Moreover, to improve the performance of the proposed algorithms, we propose a parallel solution on the Apache Spark platform, using the Streaming real-time computing module. To efficiently process the large-scale time-series datasets in distributed computing environments, Distributed Streams (DStreams) and Resilient Distributed Datasets (RDDs) are used to store and calculate these datasets. Extensive experimental results show that our PPTSP algorithm has significant advantages compared with other algorithms in terms of prediction accuracy and performance.