I can see from histogram that one of my independent variable (continuous) follows uniform distribution (very close), is there a way I can transform this variable such that it follows normal distribution?
There are plenty of ways to do so. You can find some of them from this thread: https://stackoverflow.com/questions/75677/converting-a-uniform-distribution-to-a-normal-distribution
Please review these additional resources, as well: https://stackoverflow.com/questions/45296586/how-to-convert-uniform-normality-variables-in-python, https://mathoverflow.net/questions/28557/how-do-i-convert-a-uniform-value-in-0-1-to-a-standard-normal-gaussian-distri
Log Transformation can be a good start to make the distribution normal.