Have you tested your 1/4" seam? You can Google this or do a search on the QB for more instructions. Basically you sew 3 strips of fabric together (such as 2.5" side strips), press, then measure the width (should measure 6.5" raw edge to raw edge if using 2.5" strips). If the measurement is less than 6.5", your seam allowance is too wide.
As others have mentioned, starching fabric before cutting helps a lot.
If you are pre-cutting strips to measurements, pinning should help.
Most likely your seam allowance is off and/or your seam allowance is not consistent. I use a physical barrier to keep my seam allowance consistent (in my case, strips of moleskin that I place on the bed of my machine so I have something to butt the raw edges against when I piece).