This paper proposes a new climb procedure called a gradual climb procedure. When aircraft climb to the cruise altitude or change the flight level, maximum climb thrust is usually applied. However, this maximum cruise thrust leads to a higher fuel consumption compared to the cruise thrust, which results in non fuel optimal higher climb rate. An optimal rate of climb which minimizes the fuel consumption exists, but aircraft usually opt for a faster rate of climb. This paper focuses on the part of the climb phase just prior to the cruise altitude, and clarifies the relationship between fuel consumption and the rate of climb via numerical simulations. The author also proposes a practical fuel-saving climb procedure considering actual air traffic control constraints and pilot operation. The expected fuel saving is of the order of 50 lb, which corresponds to 0.1 % of total cruise fuel consumption. However, the proposed procedure will be applicable to almost all aircraft and flights worldwide, so the cumulative effect will be significant. In addition, the negative effects to air traffic control and a pilot are minor, so the proposed gradual climb procedure can be applied in the near future operation.