This paper presents a novel 3-D full electromagnetic particle-in-cell (PIC) code called JefiPIC, which uses Jefimenko’s equations as the electromagnetic (EM) field solver through a full-space integration method. Leveraging the power of state-of-the-art graphic processing units (GPUs), we have made the challenging integral task of PIC simulations achievable. Our proposed code offers several advantages by utilizing the integral method. Firstly, it offers a natural solution for modeling non-neutral plasmas without the need for pre-processing such as solving Poisson’s equation. Secondly, it eliminates the requirement for designing elaborate boundary layers to absorb fields and particles. Thirdly, it maintains the stability of the plasma simulation regardless of the time step chosen. Lastly, it does not require strict charge-conservation particle-to-grid apportionment techniques or electric field divergence amendment algorithms, which are commonly used in finite-difference time-domain (FDTD)-based PIC simulations. To validate the accuracy and advantages of our code, we compared the evolutions of particles and fields in different plasma systems simulated by three other codes. Our results demonstrate that the combination of Jefimenko’s equations and the PIC method can produce accurate particle distributions and EM fields in open-boundary plasma systems. Additionally, our code is able to accomplish these computations within an acceptable execution time. This study highlights the effectiveness and efficiency of JefiPIC, showing its potential for advancing plasma simulations.