I came to an design that has same structure to this one(US7717717 B1). That patent claimed the inner thin plastic piece with conductive traces. My design also has same structure with the inner plastic piece, but the traces on it are designed differently and my design has additional ICs for faster speed. Can I apply for patent without infringement?
First off, infringement refers to use of an earlier patent by a later product. So no infringement occurs through your applying for a patent or even getting the patent.
Secondly, your product might infringe an earlier patent regardless of whether you have a patent or not. This can happen when your patent claim is a subset of an earlier patent claim - that is, earlier claim included elements A and B, and your patent claims A+B+C - presumably an improvement! In this case, any product (even yours!) having all elements A, B, C will infringe both patents.
Now as to your question, for your patent application you will want to find some feature T2 (hopefully your differently designed traces) that are not disclosed anywhere in the earlier patent - not in the claims, not in the written description - and put this feature T2 in your claims. Be aware that there could be some other design for the traces - let's call it T3 - that would also work - in which case a new competitor could easily design a product with T3 that would not infringe a claim written just for T2. Then it gets to a question whether you can assert that the product using T3 is equivalent to your invention - if it gets to court that could go either way. Anyway, in your patent application try to cover as much ground as you can without overlapping the other patent.
Finally, keep in mind that even if your claims with T2 are different from anything disclosed in the earlier patent, the PTO may still reject your applications because (a) it would be an obvious modification, or (b) your T2 traces are used in some other prior art and would be obvious to try. For this, try to add more features and description in your application, so you can have a fallback position to narrow your claims to something the PTO will agree to allow. Keep in mind that the narrower the claim, the less valuable it is. Also, the broader the claim, the easier it is to be invalidated by prior art.
Probably a longer reply than you need or want. Hope it helps. Good luck!