We present a multivariable coded aperture (MVCA) for lensless three-dimensional integral imaging (3D II) systems. The new configuration is based on a time multiplexing method using a variable pinholes array design. The system provides higher resolution 3D images with improved light intensity and signal to noise ratio as compared to single-pinhole system. The MVCA 3D II system configuration can be designed to achieve high light intensity for practical use as microlenslets arrays. This new configuration preserves the advantages of pinhole optics while solving the resolution limitation problem and the long exposure time of such systems. The three-dimensional images are obtained with improved resolution, signal to noise ratio, and light efficiency. This integral imaging lensless system is characterized by large depth of focus, simplicity, and low cost.