Non-autoregressive (NAR) automatic speech recognition (ASR) models predict tokens independently and simultaneously, bringing high inference speed. However, there is still a gap in the accuracy of the NAR models compared to the autoregressive (AR) models. In this paper, we propose a single-step NAR ASR architecture with high accuracy and inference speed, called EffectiveASR. It uses an Index Mapping Vector (IMV) based alignment generator to generate alignments during training, and an alignment predictor to learn the alignments for inference. It can be trained end-to-end (E2E) with cross-entropy loss combined with alignment loss. The proposed EffectiveASR achieves competitive results on the AISHELL-1 and AISHELL-2 Mandarin benchmarks compared to the leading models. Specifically, it achieves character error rates (CER) of 4.26%/4.62% on the AISHELL-1 dev/test dataset, which outperforms the AR Conformer with about 30x inference speedup.