What satisfied customers say about the Pimsleur Swahili Audio Downloads:

If you're absolutely new to Swahili (as are most humans), this audio book is a great 1st place to *start*. It will really aid in learning how to pronounce Swahili. On a trip to Kenya, a number of Kenyans commented that I sounded like a life-long native speaker. This was surprising to them mainly because my vocabulary was so poor. This audio set will NOT teach you how to speak Swahili; it will teach you how to pronounce it wonderfully - a great first step. - Redneck, Texas, USA

I'm 60 and the thought of learning a new language seemed very daunting but this Pimsleur course, broken up into ten 30-minute sessions, is very efficient and well thought out. The key is to speak each word out loud when asked, which allows your brain and your mouth to adapt to this new, melodic, and often tongue-twisting sound. 
Each new lesson reviews the last and then inserts a new word or two into sentences you already know. It focusses on words and short sentences that should be very useful when travelling and as the course proceeds you realize that you are able to invent your own sentences and express new thoughts with what you learn.
If anything, the only critique would be that some of the more difficult pronounciations should be spelled out.
Ms often sound like Ns, and Bs like Ps etc. Expect to listen to each lesson more than once, but progress is very
rapid.  -  Miggs Burroughs, Westport, CT, USA