The channels of a printed circuit heat exchanger (PCHE) can have different shapes, and the zigzag channel shape is one of the most widely used because of the relatively simple manufacturing process and low cost. However, the heat transfer enhancement of a zigzag channel is at the expense of increasing the pressure drop. In this paper, new channel shapes of a PCHE, i.e., a zigzag with an inserted straight channel and a zigzag channel with radian, were numerically investigated, with the aim of improving the heat transfer and reducing the pressure drop of supercritical LNG using the SST κ-ω model. The local and total pressure drop and heat transfer performance of supercritical LNG in a zigzag channel, zigzags with 1–5 mm inserted straight channels, and a zigzag channel with radian were analyzed by varying the mass flow rate from 1.83 × 10−4 to 5.49 × 10−4 kg/s. Performance evaluation criteria (PEC) were applied to compare the overall heat transfer performance of the zigzags with 1–5 mm inserted straight channels and a zigzag channel with radian to the zigzag channel of a PCHE. The maximum pressure drop for the zigzag channel was twice the minimum pressure drop for the zigzag channel with radian, while the convective heat transfer coefficient of the zigzag with a 4 mm inserted straight channel was higher, which was 1.2 times that of the zigzag channel with radian with the smallest convective heat transfer coefficient. The maximum value of the PEC with 1.099 occurred at a mass flow rate of 1.83 × 10−4 kg/s for the zigzag with a 4 mm inserted straight channel, while the minimum value of the PEC with 1.021 occurred at a mass flow rate of 5.49 × 10−4 kg/s for the zigzag with a 1 mm inserted straight channel. The zigzag with a 4 mm inserted straight channel had the best performance, as it had a higher PEC value at lower mass flow rates.