Based on the coupled mode theory,the electromagnetic fields in core and cladding of long-period fiber grating are analyzed using Debye potential method.The vector expression of the field components in the core and the cladding are obtained.After solving the effective refractive index and the coupling constants of the core and cladding modes,transmission spectrum is got through solving the couped mode equation by numerical integration method.The integral method is an accurate method for solving transmission spectrum.The research provides theoretical foundation for optimization and high sensitive measurement in the fields of optic fiber communications and sensors.