Can an argument with a true premises and true conclusion be invalid?

Yes. It could be a coincidence that the premises and conclusion are all true. For example, here is an argument:

1. It is true that if a person belongs to the Republican Party they must be an American.

2. Mitt Romney is an American.

3. Therefore, the conclusion is that Mitt Romney is a Republican.

Although both premises and the conclusion are true, the argument is not valid. That is because it is possible to imagine an argument in this form where the premises were true, but the conclusion is not. (Imagine if the second premise were "Barack Obama is an American" which is true, leading to the conclusion "Barack Obama is a Republican" which is false.)