Hair colors come in different tones, such as cool, neutral or warm, and each has its own base shade as well. Depending on the tone and base shade, the resulting color will have different underlying tones. In other words, not all brown hair colors are created equal. Auburn is a reddish brown color, and the trick to finding a shade of brown without auburn is choosing a brown with the right tone and base shade.
Determine your desired shade of brown -- for example, light, medium or dark.
Choose from a couple of options in order to find a brown with no auburn tone. You could select an ash brown color. Ash has a green base to it, so there won't be any red tones present. Many hair color product brands have color charts on their websites, so look at those first to find an ash color. Or go to your local beauty supply store and tell them you're looking for an ash brown color.
Go for another option if ash, which is classified as a cool color, isn't exactly what you want. Other hair colors are neutral or warm, and you could select a neutral brown instead. The box of hair color should indicate if it's a neutral base color, sometimes denoted with an "N." If you need help, consult the folks at your local beauty supply store.
Pick up an unred hair color additive product to be on the safe side. If you choose a neutral brown, there's a risk that an auburn tone could still appear when you color your hair. The additive will eliminate any red tones from coming through. You simply add it to your hair color product before applying to your hair. Follow the full instructions on the product's package.