Dynamic quality of service (QoS) data contain rich temporal patterns of user-service interactions, which are vital for better understanding user behaviors and service conditions. Canonical polyadic (CP)-based latent factorization model has proven to be capable of capturing such patterns. However, it models the relations among latent features of user, service and time in a rigid and unnatural way, causing its failures in capturing the complex patterns when the target QoS data become massive. To address that issue, this paper proposes a Biased Non-negative Tucker Factorization of 3D tensors (BNTucF) model with the four-fold ideas: (1) utilizing a core tensor for modeling the complex interactions among latent features; (2) incorporating linear biases into the model for accurate descriptions on QoS fluctuation; (3) constraining the model to be non-negative for describing QoS non-negativity; (4) deducing a single latent factor-dependent, multiplicative updating scheme for training the model in an efficient density-oriented way. Empirical studies demonstrate that the proposed BNTucF can learn complex dynamic user-service interaction patterns more accurately, hence achieving accurate predictions on missing QoS data.