追逐梦想的英文是 "pursue one's dreams" 或 "chase one's dreams"。这个短语来源于人们对于实现自己的理想和目标的努力。例如：

She is pursuing her dream of becoming a famous singer. 她正在追逐成为一名著名歌手的梦想。

He never gave up chasing his dream of starting his own business. 他从不放弃追逐属于自己的商业梦想。