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This paper proposes a new call admission control scheme considering the call dropping probability of ongoing calls in LEO satellite networks. Quality of service (QoS) provisioning of low handover failure probability is used in the proposed call admission control (CAC) scheme to guarantee predefined acceptable call dropping probability for each call. To ensure the call dropping probability the handover failure probability has been formulated using the classification of the local traffic conditions and the derivation of generation probability for the equivalent case of handover failure event. The performance of the proposed scheme has been evaluated in terms of call dropping probability and handover failure probability. The performance evaluation results have clearly shown that the proposed CAC scheme guarantees the continuity of call connections with predefined QoS levels.