Parameter learning of the state-space model (SSM) plays a significant role in the modelling of time-series data and dynamical systems. However, the closed-form inference of the parameter posterior is often limited by sequential construction and non-linearity of the SSMs, which has led to the development of sampling-based algorithms such as particle Markov chain Monte Carlo (PMCMC). We present a novel algorithm, the particle filter variational inference (PF-VI) algorithm, which achieves closed-form learning of SSM parameters while tractably inferring the non-linear sequential states. We apply the algorithm to a popular non-linear SSM example and compare its performance against two competing PMCMC algorithms.