No. Amway is a multilevel, or "network," marketing (MLM) organization that pays commissions to salespeople for the products they sell, on products sold by others they recruit and often bonuses when their teams reach a certain level of sales.
Multilevel or network marketing is different from a pyramid scheme as it is illegal, and the vast majority of participants lose money.
In an article of USA Today published on February 10, 2011, Amway was involved in a "pyramid scheme" — which was changed to "illegal scheme" in an amended version — and has agreed to pay $55 million to former distributors. But "the case was not proven" and that Amway chose to settle because they're focusing on building a healthy business.
If you decide to buy into the program and promote the products, you must be sure your marketing materials are truthful and that there's solid evidence to back up the claims you make about the products. Learn more about multilevel marketing plans at Consumer.ftc.gov.