Plasma loops are the elementary structures of solar flaring active regions which dominate the whole processes of flaring eruptions. The standard flare models are well explained the evolution and eruption after magnetic reconnection around the hot cusp-structure above the top of plasma loops, however, the early evolution of the plasma loops before the onset of magnetic reconnection has been poorly understood. Considering that magnetic-gradients are ubiquitous in solar plasma loops, this work applies the magnetic-gradient pumping (MGP) mechanism to study the early evolution of flaring plasma loops. The results indicate that the early evolution depend on the magnetic field distribution and the geometry of the plasma loops which dominates the balance between the accumulation and dissipation of energy around loop-tops. Driven by MGP process, both of the density and temperature as well as the plasma beta value around the looptop will increase in the early phase of the plasma loops evolution. In fact, the solar plasma loops will have two distinct evolutionary results: the low, initial dense plasma loops with relatively strong magnetic fields tend to be stable for their maximum beta value always smaller than the critical value, while the higher, initial dilute solar plasma loops with relatively weak magnetic fields tend to be unstable for their beta values exceeding the critical value at a time of about one hour after the formation of the solar magnetized plasma loop. The latter may produce ballooning instability and finally trigger the following magnetic reconnection and eruptions. These physical scenarios may provide us a new viewpoint to understand the nature and origin of solar flares.