Recently there has been great progress in laser-driven plasma-based accelerators by exploiting high-power lasers, where electron beams can be accelerated to multi-GeV energy in a centimeter-scale plasma due to the laser wakefield acceleration mechanism. While, to date, worldwide research on laser plasma accelerators has been focused on the creation of compact particle and radiation sources for basic sciences, medical and industrial applications, there is great interest in applications for high-energy physics and astrophysics, exploring unprecedented high-energy frontier phenomena. In this context, we present an overview of experimental achievements in laser plasma acceleration from the perspective of the production of GeV-level electron beams, and deduce the scaling formulas capable of predicting experimental results self-consistently, taking into account the propagation of a relativistic laser pulse through plasma and the accelerating field reduction due to beam loading. Finally, we present design examples for 10-GeV-level laser plasma acceleration, which is expected in near-term experiments by means of petawatt-class lasers.