The New Testament letters indicate that healings were an ongoing part of the life of the Church. Paul describes healing as a charism of the Holy Spirit given in a special way to some (1 Cor 12:9, 28, 30), but healing also occurs through prayer and anointing by church elders (Jas 5:14-15), as well as the prayer of ordinary believers (Jas 5:16). Thus the New Testament reveals the ministry of healing as a part of the normal life of the Church.
Source: Report 'Do not quench the Spirit': Charisms in the life and mission of the Church, published by the Potifical Council for Promoting Christian Unity, nr. 60