You might need to, or you might not. It depends on any elections you might have made for the LLC.
A single-member LLC is a disregarded entity in the eyes of the IRS, i.e., it doesn't exist as a taxpayer or an entity that needs to file its own income tax return. All the business activity of the LLC is deemed your business activity. Accordingly, there's no need to file a separate income tax return for the LLC, for federal purposes. (I believe states generally follow the same process here as the IRS, but you might need to prepare some sort of separate report to the state in which the LLC is organized - a report that certainly looks like an "income tax return" - so the state can assess fees for the "privilege" of having the LLC organized in that state.)
If you've made an election for the LLC to be taxed as a C-Corp or Sub-S Corp then the LLC will have to file an income tax return. A Sub-S Corp won't pay income tax but will "pass through" the corporation's activities to you on a Schedule K-1. A C-Corp will pay income tax if the C-Corp is profitable, and you'll pay income tax on any dividends received from the C-Corp.
