"Reading a book" 这个短语可以说成 "to read a book"，来源是日常英语使用中的固定用法。
下面是一些例句：
I love to read a book before going to bed.
(我喜欢在睡觉前读书)
He spends most of his free time reading a book.
(他大部分空闲时间都在读书)
She has a collection of books that she enjoys reading.
(她有一堆书，她喜欢读)