Time series forecasting (TSF) is widely used in various fields such as business, finance, science and engineering. A time series is a sequence of values or observations of variables recorded at continuous time points. One of the main purposes of time series data is that past data observations can be used to predict future values. A number of time series prediction algorithms for machine learning and statistics are proposed in literature. In Time series forecasting (TSF), there are generally two problems that haven’t been solved. One is the time-delay between the predicted values and the actual values. The other is the extreme values of the peaks and valleys of the time series. Many traditional methods such as AR, ARMA, and ARIMA and so on are well applied to solve stationary time series forecasting. However, in practical applications, time series is almost nonstationary, which restricts the stationary methods above. In fact, the majority of machine learning algorithms also have difficulty solving the two problems above. Therefore, a new peak-sensitive method focusing more attention on the observations around the peaks and valleys has been proposed. The peak-sensitive method can predict these observations around the peaks and valleys accurately and it is these observations that determine the position of the peaks and valleys. In such way, all the observations, including the peaks and valleys, are accurately predicted. Compared to Neural Networks (NNs) and Support Vector Machines (SVMs), Extreme Learning Machine is a simple and effective learning method of the single-hidden feedforward neural network (SLFN). This thesis aims to develop at first developing the peak-sensitive method partnered with ELM and kernel ELM, and second at comparing the ELM and kernel ELM to the proposed peak-sensitive method. The results shows that the proposed method can outperform the original ELM and kernel ELM in terms of coefficient of determination (R 2 ) and Root Mean Squared Error (RMSE). A time-delay index M and peak/valley hit rate (PHR/VHR) were proposed to quantify the time-delay problem and the peak/valley of the forecasting models, and experiments demonstrate that proposed method can significantly solve the time-delay problem and peak/valley problem, indicating that the proposed peak-sensitive method is a potentially promising new method of time series forecasting that merit further study.