The remarkable presence of side lobes levels in ultrasound B-mode imaging significantly decreases the image quality. Therefore, the use of an apodization function is of great importance. Linear windowing functions are among the most efficient techniques used to optimize antenna directivity by suppression of the side lobes. However, the apodization causes the degradation of lateral resolution by elevating the main lobe width. A new apodization approach that couples a linear windowing technique, and a non-linear windowing technique has been suggested. In this paper, a new dynamic apodization technique called "Dynamic Triangular Apodization" (DTA) is proposed. It enables nonlinear windowing for each imaging direction. In addition, the effectiveness of a hybrid method that combines the Hanning window with the DTA algorithm is evaluated. In order to validate the proposed method, two types of simulation are carried out; namely point spread function and cyst phantom simulation. In the point spread function simulation, the main lobe width of the dual-apodization algorithm is very similar to that of the rectangular window and at the same time, the side lobes levels are significantly reduced. In the cyst target simulation, the Contrast to Noise Ratio (CNR) values of the dual apodization are significantly improved. The performance of the non-linear apodization is numerically investigated. In comparison with the rectangular window, the non-linear apodization method called DTA-Hann maintains low side lobes levels without altering the main lobe width. Consequently, it is a promising technique that aims to ameliorate the image quality.