The deregulated electricity market and growing electricity demand are increasing the need for electrical load forecasting models. Accurate forecasts help market participants to plan, manage and control electricity systems. In the master's thesis we deal with the problem of forecasting the electricity consumption of all customers with a connection power of less than 43 kW. This includes households and small businesses. Electricity consumption will be predicted using Gaussian process model which is based on Bayesian statistics. We introduce two views to interpret Gaussian process regression models; function space view and weight space view. The result of Gaussian process is the normal probability distribution determined by mean and variance. The mean represents the most probable output value and the variance gives us information about confidence in the predicted output value. An energy demand is driven by many variables. A study of input variables was made to check which variables should be included in our model. We implemented this model using the Python's machine learning library, i.e. Scikit-Learn. Model was tested on the electrical load from a distribution network Elektro Ljubljana, d.d.