The best way to go about losing something inherent in your personality is to accept the fact that it is a part of you. Since English wasn’t developed with a universally applicable way of speaking it, people in different regions often speak it with a regional accent, which is often a derivative of their mother tongues. Once you realize you have an accent, you can start taking steps to learn diction and pronunciation not regional to you. An interesting truth however is that people who speak English as their mother tongue actually like people speaking with a slight accent!
Let’s discuss how to go about losing the accent. First thing you need to do is to record your voice on a tape in a casual tone, preferably when talking to someone or reading aloud. A tape recording will tell you where and how you have an accent. Concentrate on where you stress and when you needlessly elongate vowels, and then try to consciously avoid doing it. During speaking, when you realize you are going to pronounce a stress point, slow down and speak deliberately instead of going fast, because talking at speed makes losing the regional accent difficult. When you counter words which are accentuated, speak them out slowly, and speaking them correctly will become easier with practice.
Take care while talking to people who also have an accent, because listening to theirs will bring out yours involuntarily. Instead, try mimicking those people and accent whom you want to speak, so that regular pronunciation of words in the correct way becomes habitual. Listening to news anchors also helps, because they are trained to lose their regional accents and speak in a non-regional diction. Try repeating their manner of speaking to your self, paying attention to the way different vowels and consonants were pronounced by the anchors.
When you follow these steps, tape record your voice regularly after a few days and listen to the playback. This is the only way you can check your progress, by comparing your latest tape with the first one you recorded. With time, your accent will fade away and you shall speak fluently.