For the type of swing you have, there should be no problems with your child sleeping in it as long as you follow the safety precautions of strapping them in.
I have had multiple conversations with our pediatrician about where our daughter can safely sleep. From one-week-old through her current one-month-old, she has successfully slept in her crib twice. Every other time we have tried has resulted in her waking up in a fit of colicky rage. Thus we have had to accept other options.
Most of the time, she sleeps in our arms, as this is the only consistent easy for us to get her to stay asleep. The second-most common option is sleeping in her swing, which is a variation on the same design you have here (a Fischer Price model with a fully reclining option).
Our pediatrician specifically stated that this option was OK as long as she was strapped in. Further, Dr. Karp's "Happiest Baby on the Block" specifically states that sleeping in a swing is OK.