The performance of neuromorphic computing (NC) in executing data-intensive artificial intelligence tasks relies on hardware network structure and information processing behavior mimicking neural networks in the human brain. The functionalities of synapses and neurons, the key components in neural networks, have been widely pursued in memristor systems. Nevertheless, the realization of neuronal functionalities in a single memristor remains challenging. By theoretical modeling, here we propose asymmetric ferroelectric tunneling junction (AFTJ) as a potential platform to realize neuronal functionalities. The volatility, a necessary property for a memristor to implement a neuron device, is enhanced by the co-effect of polarization asymmetry and Joule heating. The simulated polarization reversal dynamics of the AFTJ memristor under trains of electric pulses reproduces the leaky integrate-and-fire functionality of spiking neurons. Interestingly, multiple spiking behaviors are found by modulating the pulse width and interval of trains of electric pulses, which has not yet been reported in ferroelectric neuron. The influences of several key factors on the neuronal functionalities of AFTJ are further discussed. Our study provides a novel design scheme for ferroelectric neuron devices and inspires further explorations of ferroelectric devices in neuromorphic computing.