A new hybrid model combining the kernel functions along with the random vector functional link neural network (RVFLN) is proposed in this paper for an effective solar power prediction. The conventional RVFLN is known for its fast learning speed, simple architecture and good generalization capabilities and allows direct connection between input and output nodes along with nonlinear enhancement nodes with random weights. However, the bottleneck of selecting the number of hidden enhancement nodes and mapping functions is still a challenging problem. To overcome these deficiencies of the conventional RVFLN, kernel functions are used for both the direct links and the hidden nodes to provide better stability, generalization and regression accuracy. Instead of using a single kernel for the enhancement nodes, this paper proposes an optimal kernel function that comprises a linear combination of weighted local kernel and a global kernel to improve the prediction accuracy of the solar power generation. This optimal kernel will be known as multi-kernel RVFLN (MK-RVFLN), and its parameters are optimized using an efficient metaheuristic evaporation-based water cycle (EVWCA-MKRVFLN) to provide accurate prediction of solar power. To validate its superior prediction accuracy, two solar power plants of 25 and 100 MW capacity in the states of New York and California are considered for 5-min- and 60-min-ahead prediction in the months of January, April, July and October. The result analysis shows that the MK-RVFLN algorithm attains better performance than many other techniques.