You're thinking of "Gadsby,"a novel by Ernest Vincent Wright, written around 1939. It is famous for not containing the letter 'e'.
The lack of the letter 'e' makes Gadsby a lipogram, or an example of constrained writing. Wright explains in the introduction that he had to tie down the 'E' key of his typewriter to avoid mistakes.
The story tells how the main character, John Gadsby, transforms his home town of Branton Hills into a bustling city by tapping the vigour and original thought of youth. Quoting from its first paragraph:
"If youth, throughout all history, had a champion to stand up for it; to show a doubting world that a child can think; and, possibly, do it practically; you wouldn't constantly run across folks today who claim that "a child don't know anything." A child's brain starts functioning at birth; and has, amongst its many infant convolutions, thousands of dormant atoms, into which God has put a mystic possibility for noticing an adult's act, and figuring out its purport."
The use of odd punctuation, contrived language, and disjoint air carry on throughout the book.
As well as having to avoid common words such as 'the', 'he', and 'she', Wright made the task particularly hard for himself by setting Gadsby in the past tense, while avoiding the verb ending '-ed'. He also made valiant attempts to include objects that ordinarily require the letter E, such as a horse-drawn fire engine; he achieved this by describing the object without quite naming it.
Wright never saw his work in print - he died at the age of 66 on the day it was published.
A similar lipogrammatic book is Georges Perec's La Disparition (1969), which was later translated into English by Scottish author Gilbert Adair as A Void (1994).