Halbach array is a popular permanent magnet array used in head dedicated portable MRI. It supplies transversal main magnetic field (B0), and it works well with solenoid RF coils when B0 inhomogeniety is small. The B0 a Halbach array supplies is low. To compensate this, it is desired to have a high coil sensitivity of the solenoid coil that works in such a system. Hence in this paper, an asymmetrical tapered solenoid was proposed and an optimization was carried out for both the coil profile and pitches between turns for high coil sensitivity and homogeneity. Multi-objective genetic algorithm was used. The optimized solenoid coils are constructed and compared with a reference coil of comparable dimension. The optimal design shows B1 field increase of ∼33% and minimal tradeoff in homogeneity of ∼10 %. The measured results are in good agreement with simulated and calculated results.