A new construction method of two-dimensional (2D) variable-weight optical orthogonal codes (VWOOCs) is proposed for high-speed optical code-division multiple-access (OCDMA) networks supporting multiple qualities of services (QoS). The proposed codes have at most one-pulse per wavelength (AM-OPPW) property. An upper bound of the codeword cardinality of the 2D VWOOCs with AM-OPPW property is derived. It is then shown that the constructed codes have ideal correlation properties and optimal cardinality. Moreover, the code length and the bit-error-rate (BER) performance of the proposed codes are compared with those of the codes proposed previously.