A numerical investigation of depressed cladding photonic crystal fiber (PCF) that has been buried in bulk lithium niobate crystal material by direct femtosecond (fs) laser writing. The leading guide of light propagation is elucidated through the photonic crystal that is embedded in a lithium niobate. The induced refractive index, confinement losses, and dispersion are numerically calculated according to the orientation of the crystal and the structure geometry of the PCF. This structure supports single and highly multimode TE and TM wave guidance at the communication wavelength 1.55µm. We realized that the confinement losses are less than 1dB/cm for both polarizations, and the transmission properties appear good for several PCF applications.