Transmitter dispersion eye closure quaternary (TDECQ) is a vital metric to characterize the quality of four-level pulse amplitude modulation (PAM-4) optical signals. However, the traditional TDECQ assessment scheme is complex and time consuming, with heavy iterative operations. Therefore, accelerating the TDECQ assessment has great significance for photonic data-center interconnection (DCI) applications. Here, we propose and experimentally demonstrate a TDECQ assessment based on linear-convolutional neural network (L-CNN) with the 1 × 1 convolutional kernel to reduce the implementation complexity. Our experimental results verify that the lightweight L-CNN can realize the accurate TDECQ assessment, without the involvement of nonlinear activation functions (NAFs). The mean absolute error (MAE) of 26.5625 and 53.125 GBaud PAM-4 signals are 0.16 dB and 0.18 dB, respectively, over a TDECQ range from 1.5 to 4.0 dB. Meanwhile, in comparison with existing CNN-based schemes, the L-CNN based TDECQ assessment scheme only needs 2048 multiplications, which have been reduced by five orders of magnitude.