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Neuroevolution has greatly promoted Deep Neural Network (DNN) architecture design and its applications, while there is a lack of methods available across different DNN types concerning both their scale and performance. In this study, we propose a self-adaptive neuroevolution (SANE) approach to automatically construct various lightweight DNN architectures for different tasks. One of the key settings in SANE is the search space defined by cells and organs self-adapted to different DNN types. Based on this search space, a constructive evolution strategy with uniform evolution settings and operations is designed to grow DNN architectures gradually. SANE is able to self-adaptively adjust evolution exploration and exploitation to improve search efficiency. Moreover, a speciation scheme is developed to protect evolution from early convergence by restricting selection competition within species. To evaluate SANE, we carry out neuroevolution experiments to generate different DNN architectures including convolutional neural network, generative adversarial network and long short-term memory. The results illustrate that the obtained DNN architectures could have smaller scale with similar performance compared to existing DNN architectures. Our proposed SANE provides an efficient approach to self-adaptively search DNN architectures across different types.