Via-holes transition is an important component in multi-layer microwave and millimetre wave circuit systems, directly affecting signal transmission performance. In order to improve the millimetre wave performance of via-holes transition, the electromagnetic design automation software has been used to optimise the circuits design, which could consume a plenty of computer resources. In recent years, deep neural network (DNN) has been widely applied in the research of microwave component and is expected to solve this challenging and time-consuming problem. Employing large labelled datasets to obtain high-performance DNN model is desired but troublesome. Therefore, a transfer learning with deep neural network (TLDNN) surrogate model is proposed to improve the modelling efficiency. The experimental validation demonstrates that, compared with the conventional DNN, the TLDNN can reduce the amount of training data required without losing accuracy and accelerating modelling speed for behaviour prediction of via-holes transition. A prototype via-holes transition fabricated on multilayer liquid crystal polymer (LCP) substrate exhibits an average S11 deviation of less than 2.9 dB between the measured and predicted results.