Aiming at the data security problem in big data environment, in this paper we propose a new chaotic encryption algorithm based on both big data platform named Hadoop and non-degenerate high-dimensional discrete hyperchaotic system. The algorithm utilizes the chaotic stream cryptography and reads the data from HDFS of Hadoop platform. After fragmentation processing and MapReduce programming, the data are encrypted and decrypted by Map function in parallel. The Reduce function implements the merging operation of the data and stores them on the HDFS. The algorithm has a better execution efficiency. Compared with the low-dimensional chaotic system based encryption algorithm, the non-degenerate high-dimensional discrete chaotic system based encryption algorithm can improve the system security performance. It can pass the strict TESTU01 test with better statistical properties and make sure that the correlation with the parallel ciphertext is very small. Numerous key parameters increase the difficulty in making estimation or identification. Under the closed-loop feedback in ciphertext, it has the ability to resist the known and chosen plaintext attacks.