Daily peak load forecasting is crucial for the operation of bulk power systems, including economic dispatch and unit commitment. It is also essential for peak load shaving and load management in distribution systems. In power markets, peak load forecasting helps participants develop bidding strategies. This paper proposes a new method, using a hybrid convolutional neural network (CNN) that is cascaded with a fully-connected network, for making week-ahead daily peak load forecasts. The proposed method uses three loops to obtain the optimal CNN: The outer loop performs crossover/mutation operations and tournament selection to produce chromosomes to optimize the network topology and hyperparameters (such as kernel size) of the hybrid CNN by genetic algorithms; the middle loop deals with the order of chromosomes; the inner loop optimizes the synaptic weights and parameters (e.g. values of a kernel) using Adam optimizer. Daily peak load data and corresponding meteorological data for Taiwan are explored. Simulation results show that the proposed method outperforms the traditional CNN, multi-layer neural network, recurrent neural network, support vector regression and vector autoregressive moving average model.