The use of water-soluble chemical fertilizers for years under drip irrigation conditions results in soil compaction, fertility decline, and fruit quality decrease in arid areas. Currently, little research has been reported regarding the effects of increasing organic fertilizer and reducing drip chemical fertilizer on the growth of grape plants under different conditions in arid areas. In this study, five different treatments were conducted. Compared with no fertilizer for 3 consecutive years (CK) and single fertilizer for 3 consecutive years (T0), organic fertilizer plus 1 year of reducing drip chemical fertilizer (T1), organic fertilizer plus 2 years of reducing drip chemical fertilizer (T2), and organic fertilizer plus 3 years of reducing drip chemical fertilizer (T3) improved the soil pH, electrical conductivity (EC) values, and soil organic matter content to different degrees during early growth stages (15 days after anthesis) and mature stages (75 days after anthesis). The available N, P, and K contents in the T1 and T2 treatments increased significantly. With the T2 treatment, the longitudinal and transverse diameters of the ‘Summer Black’ grapes were the largest during the two fruit expansion periods. The anthocyanin content of grape peel with the T2 treatment was 22.0% higher than that with the T0 treatment. The soluble solids, sugar–acid ratio, various sugar contents, vitamin C, and total phenol of the fruit increased significantly with the T2 treatment, indicating that the T2 treatment was best for promoting grape growth and fruit quality and that the T3 treatment was the second best.