Например:

func main() {
	router := gin.New()
	// LoggerWithFormatter middleware will write the logs to gin.DefaultWriter
	// By default gin.DefaultWriter = os.Stdout
	router.Use(gin.LoggerWithFormatter(func(param gin.LogFormatterParams) string {
		// your custom format
		return fmt.Sprintf("%s - [%s] \"%s %s %s %d %s \"%s\" %s\"\n",
				param.ClientIP,
				param.TimeStamp.Format(time.RFC1123),
				param.Method,
				param.Path,
				param.Request.Proto,
				param.StatusCode,
				param.Latency,
				param.Request.UserAgent(),
				param.ErrorMessage,
		)
	}))
	router.Use(gin.Recovery())
	router.GET("/ping", func(c *gin.Context) {
		c.String(200, "pong")
	})
	router.Run(":8080")
}

Образец вывода

::1 - [Fri, 07 Dec 2018 17:04:38 JST] "GET /ping HTTP/1.1 200 122.767µs "Mozilla/5.0 (Macintosh; Intel Mac OS X 10_11_6) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/71.0.3578.80 Safari/537.36" "