At SuperKEKB, the maximum beam currents and the luminosity could be limited by the beam injection in the near future. We estimated requirements to the beam injection to achieve the next target luminosity of 1 × 1035cm-2s-1. Two cases of β y * = 1 mm and 0.8 mm are considered. A simulation shows that we need to suppress the emittance growth of the injecting positron beam in the beam transport (BT) line down to its design value to meet the requirement with β y * = 1 mm. In the case of β y * = 0.8 mm, we need to improve dynamic aperture of LER in addition to the suppression of the emittance growth. Efforts to improve the beam quantity and quality in LINAC and in BT are summarized. The present most serious problem concerning quality of the injecting beams is emittance growth in the BT lines for both electron and positron beams. Simulations and experiments show that the effects of ISR and CSR in the BT lines cause a large horizontal emittance growth of the electron beam. Several measures to suppress the emittance growth are under considerations.