This paper investigates efficient beam search techniques for end-to-end automatic speech recognition (ASR) with attentionbased encoder-decoder architecture. We accelerate the decoding process by vectorizing multiple hypotheses during the beam search, where we replace the score accumulation steps for each hypothesis with vector-matrix operations for the vectorized hypotheses. This modification allows us to take advantage of the parallel computing capabilities of multi-core CPUs and GPUs, resulting in significant speedups and also enabling us to process multiple utterances in a batch simultaneously. Moreover, we extend the decoding method to incorporate a recurrent neural network language model (RNNLM) and connectionist temporal classification (CTC) scores, which typically improve ASR accuracy but have not been investigated for the use of such parallelized decoding algorithms. Experiments with LibriSpeech and Corpus of Spontaneous Japanese datasets have demonstrated that the vectorized beam search achieves 1.8x speedup on a CPU and 33x speedup on a GPU compared with the original CPU implementation. When using joint CTC/attention decoding with an RNNLM, we also achieved 11x speedup on a GPU while maintaining the benefits of CTC and RNNLM. With these benefits, we achieved almost real-time processing with a small latency of 0.1x real-time without streaming search process.