As an important component of the rotating machinery, rolling bearings usually work under the condition of variable speed and load, and vibration signals in the same health state are significantly different due to the change in operating conditions. To address the problem that the existing deep learning (DL) methods have fixed nonlinear transformations for all input signals in cross-domain fault diagnosis, we propose a new activation function, i.e., parameter-free adaptively rectified linear units (PfAReLU). The proposed activation function performs adaptive nonlinear transformations according to the input data and can better capture the fault features of vibration signals in the same fault state under different operating conditions. Furthermore, the number of PfAReLU parameters is zero, so that the risk of network overfitting is reduced. At the same time, deep parameter-free reconstruction-classification networks with PfAReLU (DPRCN-PfAReLU) are also constructed for cross-domain fault diagnosis. Specifically, DPRCN-PfAReLU consists of a shared encoder, a target domain decoder, and a source domain classifier. The shared encoder adds a parameter-free attention module at the output to enhance the weight of domain-invariant features without increasing network parameters. The shared encoded representation of source domain and target domain is learned by target domain decoder and source domain classifier. Compared with other methods under nine different operating conditions via real experiment studies, the proposed method shows superiority for cross-domain fault diagnosis.