If your problem is worst at the lower frets, then there is a good chance your string height at the nut is too high. This makes the fretted notes on frets 1-5 (especially) too sharp, the problem reduces as you go up the neck. Manufacturers usually make the nut slots too shallow, except on more expensive models.
To check this, hold a string down between the 2nd and 3rd frets. Now tap the string over the first fret to see how far it moves down onto the fret. If the movement is more than the tiniest of fractions, your nut slot could do with deepening. If you can't tell this way, can you slide a piece of ordinary printer paper under the string at the 1st while fretting between 2 and 3? If the paper slides easily with no resistance, you're way too high.