Meeting a trouble in my pure sine wave inverter.

So, the waveform with the transformer is measured where? At the secondary? If yes, then it looks like your primary windings are phased incorrectly.
Cany you also share the specs of the transformer as you ordered it?
Also please try measuring the gate waveforms with a load, and with two load resistors instead of the two halves of the primary.

Hi,

Did you check it with a signal generator to make sure it can handle the primary voltage level needed?