The mission of the Holy Spirit has aspects that with the advancement of theology have gained more attention by theologians and the diverse Christian traditions. Jurgen Moltmann, among a large number of theologians, develops an original and complex reflection on the Holy Spirit, beginning with his famous Theology of Hope and having as its apex the production of the book The Spirit of Life, a work that he dedicates exclusively To reflection on the Holy Spirit. He will produce a Pneumatology that will be guided by his conception of Christian eschatology and by the biblical texts of the Apostle Paul. This research has as main objective to make an approach on how Jurgen Moltmann presents / displays the relation between the Holy Spirit and the Christian Hope taking as starting point the theological nods that it builds in the Theology of the Hope. Our approach will be divided into three different steps. At first, we will devote ourselves to presenting the main texts produced by theologians in reflecting on the Holy Spirit. Then this work will make a presentation of the main aspects of Pneumatologia moltmanianna through his main works. The final step is to discuss how Jurgen Moltmann understands the relationship between the Holy Spirit and Christian Hope. After the research, we conclude that our author produces a Pneumatology that must be read from the Eschatology that he promotes in his Theology of Hope. The Holy Spirit is understood as the life-giving power of God, which enables men and women to experience the promises of the future with God, partially, still in the present. He ensures that they will be fulfilled and propels the Church, which lives in this hope of a full realization of what has been promised, to walk within history by signaling the coming Kingdom through its actions.