Ok, so what is happening is that you are adding too much sodium hydroxide. We know this because just enough to neutralise the acid would turn the indicator green and more than enough would make the solution alkali and turn the indicator purple and then blue.
It should only take 1.5cm3 (not exactly because you don't know the exact concentration of hydrochloric acid) of 1M sodium hydroxide to neutralise 0.1M hydrochloric acid. If you must use these concentrations try going only one drop at a time and swirl the solution between drops.
If you are able to choose a different concentration of sodium hydroxide to use in the burette I would go for 0.1M. This would mean you would need about 15cm3 of the sodium hydroxide and would be a much easier volume to deal with.
Let me know how you get on.
All the best,
Mr Lawlor