I have a dataset with one dependent (continuous) variable that is not normally distributed and three independent (continuous) variables.I would like to run GLM with one dependent variables against three independent variables. Can I run a GLM without factor (categorical variable) as an independent variable?
Absolutely, you'll want to run a GLM based on a Gaussian distribution for continuous data (For count data you want to use a Poisson distribution). For a Gaussian (normal) distribution it doesn't matters if your continuous variable is not normally distributed. The assumption is the errors from the model are normally distributed. GLM covers regression methods for many types of data: continuous, count, categorical, binomial etc. The important part is that you select the right distribution type for the link function.
See here for more details: https://en.wikipedia.org/wiki/Generalized_linear_model