A compact side-pumped solar laser design is proposed to improve the TEM00-mode solar laser output performance substantially. A double-stage secondary concentrator was composed of a rectangular hollow pipe and a 2V-shaped dry pump cavity, which couples and redistributes the concentrated solar radiation from the focal zone of a 2 m diameter parabolic mirror into a grooved Nd:YAG rod. The solar laser performance was numerically optimized by both ZEMAX® and LASCADTM software. Maximum TEM00-mode solar laser power of 32 W was numerically calculated for a 4.5 mm diameter, 34 mm length grooved Nd:YAG rod, corresponding to 10.7 W/m2 collection efficiency. This value is 1.25 times more than the numerical record. Laser beam brightness figure of merit of 31.4 W was numerically attained, which is 1.84 times more than the numerical record. The proposed laser head scheme has a simple and compact design, as compared to previous schemes. Good TEM00-mode solar laser thermal performance was also numerically demonstrated.