Yes, it is. It extends Random, which always had a de facto threadsafe implementation, and, from Java 7, explicitly guarantees threadsafety.
If many threads are using a single SecureRandom, there might be contention that hurts performance. On the other hand, initializing a SecureRandom instance can be relatively slow. Whether it is best to share a global RNG, or to create a new one for each thread will depend on your application. The ThreadLocalRandom class could be used as a pattern to provide a solution that supports SecureRandom.