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Consensus-based estimators have been applied in the state estimation for cooperative multi-sensor systems, and most of current studies are for the continuous-time or discrete-time case. With regards to some engineering applications, such as ballistic target tracking, it is more suitable to adopt the continuous-discrete state-space model to formulate a dynamic system, which can capture the evolution characteristics of this state process more accurately. This paper presents a novel consensus continuous-discrete Gaussian filtering (CCDGF) estimator. On the basis of strong Taylor approximation for continuous state, the estimator utilizes the fully symmetric interpolatory quadrature (FSIQ) rule to numerically resolve the first two moments of propagated Gaussian density. Then, the average consensus protocol is leveraged to iterate the local innovations of Gaussian filtering framework at each sensor. The consensus estimates with odd-degree accuracy can be obtained through sufficient exchanges of neighborhood information. Finally, it is demonstrated by simulation examples that the CCDGF estimator can achieve performance close to its centralized counterpart, and has higher tracking accuracy with the increase of quadrature degree.