Failure prognostic predicts the remaining useful life (RUL) of machine/components, which will allow timely maintenance and repair leading to continuous reliable and safe operating conditions. In this article, a novel hybrid RUL prediction approach is proposed for heavy-duty gas turbines. Two common failures, namely the fouling in the gas turbine compressor and filter defect, are investigated. First, a discrete wavelet transform (DWT) is applied to real-time measurements to reduce the effect of noise. A parallel structure consisting of a Laguerre filter and neuro-fuzzy is then constructed to identify nonlinear failure dynamics and generate residuals. These residuals are then utilized to estimate the failure severity. Following that, Bayesian theory is employed to predict the RUL. A novel feature of the approach is that the Laguerre filter is designed by using orthogonal basis functions (OBFs), which deliver precise estimates. Another benefit is that the proposed parallel configuration accurately identifies failure dynamics and boosts the RUL prediction performance. Experimental test studies on heavy-duty gas turbines indicate the high efficiency of the proposed RUL estimation in comparison to other failure prognostic strategies.