Automatic Speech Recognition services (ASRs) inherit deep neural networks' vulnerabilities like crafted adversarial examples. Existing methods often suffer from low efficiency because the target phases are added to the entire audio sample, resulting in high demand for computational resources. This paper proposes a novel scheme named FAAG as an iterative optimization-based method to generate targeted adversarial examples quickly. By injecting the noise over the beginning part of the audio, FAAG generates adversarial audio in high quality with a high success rate timely. Specifically, we use audio's logits output to map each character in the transcription to an approximate position of the audio's frame. Thus, an adversarial example can be generated by FAAG in approximately two minutes using CPUs only and around ten seconds with one GPU while maintaining an average success rate over 85%. Specifically, the FAAG method can speed up around 60% compared with the baseline method during the adversarial example generation process. Furthermore, we found that appending benign audio to any suspicious examples can effectively defend against the targeted adversarial attack. We hope that this work paves the way for inventing new adversarial attacks against speech recognition with computational constraints.