This can happen if the amperage used on the circuit approaches that of the circuit breaker. (Electric motors use more electricity to start up.)
What is the amperage listed on the label of the dryer.
What else does it say on the label?
What amperage is listed on the circuit breaker?
If you have the instructions for the dryer, what amperage and type of circuit does it say to use for this dryer? (Does it say "time delay fuse/breaker"?)