We develop a new approach to analyze high-dimensional spatial point patterns. Among models for a spatial point process, the Log-Gaussian Cox Process (LGCP) is commonly used, which can be represented using a hierarchical modeling structure. However, fitting this model can be computational intensive often requires the use of Metropolis-Hastings. In particular, Bayesian inference of a continuous Cox processes often requires expensive Markov Chain Monte Carlo (MCMC) posterior simulation methods. We focus here on a new Bayesian method, and propose the use of a new class of prior distributions, which leads to conjugate full-conditional distributions within a Gibbs sampler that are computational straightforward to simulate from. We demonstrate the proposed methodology through simulated examples and an analyses based on a real dataset.